PcGets Basic Help

Dialogs and menus

Menus
File menu
Model menu
Test menu
Help menu

Dialogs
Formulate a model
Model Settings
Estimate a model
Recall a model
Options (Expert user's strategy)
Progress
Store in database
Subset test
Zoom sample

Model formulation and estimation
Model formulation
Modelling strategy specification
Model estimation
Progress

Model evaluation
Graphic analysis
Dynamic analysis
Recursive analysis
Forecasting
Omitted variables
Tests for linear restrictions
Estimation output

Help
Help
PcGets overview
Batch language

Activating PcGets

Start GiveWin, and start PcGets from the Modules menu.

Next, load the dataset into GiveWin, formulate the model, specify your selection strategy, estimate and analyse the results with the options from the test menu.

File Menu

Always on Top: This menu item toggles the always on top status. When switched on, PcGets will always be above other windows, even if it does not have the focus. When PcGets is shrunk to a small window, this could be useful to allow easy access. When off, the PcGets will behave as a normal window.
Note that the setting is persistent between runs.
Exit: Exits the application.

Model Menu

The Model menu allows you to formulate and estimate models, recall a previously estimated model, check the progress made in the modelling process.

The following commands are available:

Formulate
Model Settings
Estimate
Model Options
Progress

Test Menu

The Test menu is used to evaluate the model graphically, and through diagnostic testing.

Graphic analysis
Recursive analysis
Dynamic analysis
Forecast
Exclusion restrictions
Linear restrictions
Omitted variables

It also offers facilities to print out the model, generate batch files and store results/

LaTeX output
PcGets settings report
PcGets batch (General)
PcGets batch (Specific)
PcGive batch
PcFiml batch
Store in database

Help Menu

Press the F1 key for help. Or click on the Help menu and select Help Topics to see the help index.

Read the PcGets overview.

Press F1 or click on the Help button in any dialog for context-specific help.

PcGets is an empirical econometric modelling program, which interfaces with GiveWin. Thereby, it offers an extensive range of data transformations preliminary data analyses such as correlations (data means, standard deviations, 3rd and 4th moments), normality tests, unit root tests, graphing and the creation of lags.

Model formulation is straightforward, and earlier models can be recalled and revised. A batch language provides easy storage and recall of model specifications between runs.

Sample sizes are easily set or altered, including reserving observations for forecasting. Among the available estimators for linear models are Ordinar Least Squares, Instrumental Variables and their Gets generalizations.

PcGets is strongly focused on graphical information. Output can be analysed graphically, including residual histograms and densities, and their spectral densities..

Dynamic model analyses are provided including a calculation of the roots of the lag polynomials.

Recursive graphics provide a quick review of such estimators, which are useful for examining parameter constancy.

A set of diagnostic tests is evaluated for determining model adequacy, including tests for autocorrelation, various forms of heteroscedasticity including auto-regressive conditional (ARCH) and non-normality. Encompassing tests of non-nested reductions are conducted and tests for omitted variables provided.

The PcGets algorithm allows for the necessary flexibility by adjustments to the model settings. Finally, expert user's can define their personalized model selection strategies with help of the options dialog.

Formulate

Use this dialog for single equation Dynamic Model Formulation: to formulate a new model, or reformulate an existing model.

Database

Mark all the variables you wish to include in the new model or add to the existing model, in this Multiple-Selection List box, using the spacebar or the mouse.

After you have pressed Enter (or double-clicked if you are using a mouse), you can select a lag length for each variable (see lagged variables).

The variable at the top of the list will by default become the endogenous (Y) variable. To select a different dependent variable, see below.

Special

Constant
A constant will be added automatically in a new model but can be deleted.
Trend
The trend has value 1,2,3,... with value 1 occurring for the first observation in the database. This may be different from the first observation in the estimation sample, for example when using lags (of course, this only affects the value of the constant term).
Seasonal
Seasonal is only present if the database has a non-annual frequency s. Selecting this variable will lead to s - 1 seasonals being added when a Constant is present in the model (s otherwise). For example, for quarterly data, this adds:
Seasonal (1 in quarter 1, zero otherwise),
Seasonal_1 (1 in quarter 2, zero otherwise),
Seasonal_2 (1 in quarter 3, zero otherwise).
CSeasonal
This behaves as Seasonal, except that the variable has zero mean within a year. For quarterly data, for example, CSeasonal has value 0.75 in the first quarter, and -0.25 in the remaining quarters.

Model

This Multiple-Selection List box shows the current model.
The variable at the top of the list will by default become the endogenous (Y) variable.
To select a dependent variable which is listed further down:

mark the current dependent variable and clear its status;
mark the new variable, and press the Y:Endogenous button.

If you have marked variables in the model, you can delete them, or assign a status to them.

Delete

Deletes the current model selection.

New model

Deletes the whole model, so that you can start from scratch.

Clear

Clears the status of all selected model variables. Cleared variables behave as Z variables. You can also double click on a model variable to clear its status.

Y: regressand

Label the currently selected variables as the regressand (this is not possible for lagged variables). The regressand is marked by Y in the model list. Only one variable can have this status.

X: regressor

Marks the selected model variables as an unmodelled variable. This is the default for an unmarked variable, so a X variable or unmarked variable are treated in the same way.

F: fixed

Forces the selected model variables to be included in the specific model for GETS/GETSIVE.
In the case of OLS/IVE, F variables and X variables are treated in the same way.

E: endogenous

Label the current model selection as endogenous variables Endogenous variables are preceded by E in the model list. Estimation requires at least as many additional instruments as endogenous regressors in the model.

A: instrument

Label the current model selection as additional instruments. This button is only relevant if you wish to do an Instrumental Variables estimation. Additional instruments are followed by A in the model list.

OK or Add

If there are still database variables marked, this button will be called Add. Press it to add the variables (or press Deselect All to change it to OK). You will be prompted for a lag length if it is set to query. You can also double click on a database variable to add it to the model.
Press OK to move to the Model Settings or Estimation.

Cancel

Equivalent to pressing Esc, it will abort the model formulation.

Lag length

Choose one of

Query: a dialog box will prompt for a lag length when variables are added to the model.
Or specify the default lag length to use (this is persistent between runs of PcGets).

Model formulation

A dynamic equation is specified as an autoregressive-distributed lag model:

B₀(L) y_t = c + B₁(L) x_1,t + B₂(L) x_2,t + ... + B_k(L) x_k,t + e_t, t = 1,...,T. (1)

In (1), the lag polynomials are defined by:

B_i (L) = Sⁿⁱ_j=mi b_i,j L^j with 0 £ mi £ ni, i = 1,...,k.

`Solving' (1) yields:

y_t = S^k_i=1 H_i (L) x_it, where H_i (L)=B_i (L) / B₀(L). Zero is a legitimate order for a lag polynomial. Thus, static or dynamic models are equally easily specified.

A model in PcGets is formulated by:

Which variables are involved;
The orders of the lag polynomials;
The status of variables (only when it is not legitimate to treat all regressors as valid conditioning variables, and you wish to use Instrumental Variables).

When a model has been formulated, it can be estimated and then analyzed. PcGets facilitates a general-to-specific modelling strategy.

Lags

When creating lags, PcGets appends the lag length as extra characters in a name, preceded by an underscore. E.g. CONS_1 is CONS one period lagged.

Lagging a variable leads to the loss of observations, but seasonals can be lagged up to the frequency without loss. PcGets handles variables in models through lag polynomials.

Sample periods are automatically adjusted when lags are created.

PcGets stores the lag information, and uses it to recognize lagged variables for Dynamic Analysis. Lags created this way are not physically created, and do not consume any memory. However, when you compute a lag using the calculator, a new variable will be created in the database, which will NOT be treated as a lagged version of that variable, but as any other variable.

Zoom sample dialog box

Selection sample: Enter the sample period you wish to use, e.g. 1960 1 to 1980 4.

The maximum sample, which is the default, is given one line up.

Recall dialog box

Use this dialog to recall a previously estimated model.
You will have to re-estimate it to get access to the items on the Test Menu.

Models: Move the cursor to the model you wish to recall, and press OK.
Previous, Next: Use these buttons to move between the estimated models.

Model Settings dialog box

This dialog is for specifying the PcGets algorithm.

PcGets testimation algorithm

Outlier correction
F presearch testing (lag order preselection)
F presearch testing (top - down)
F presearch testing (bottom - up)
Sample split analysis
Sample-size adjusted significance level
Research strategy

Liberal strategy (Minimize non-selection probability)
Conservative strategy (Minimize non-deletion probability)
Expert user's strategy (as defined in Options)
Reporting

Report only the finally selected model
Write each iteration (condensed)
Write each iteration (detailed)

Outlier correction

If `outlier correction' is on, outliers are detected using the size of the residuals of the GUM and dummy variables are added to the model.

F presearch testing (lag order preselection)

If `lag order pre-selection' is on, an F-test checks the longest-lag blocks till the null is rejected.

F presearch testing (top - down)

If `top-down' is on, the t-test statistics are ordered from the smallest up and a cumulative F-test checks increasing block sizes till the null is rejected.

F presearch testing (bottom - up)

If `bottom-up' is on, an F-test checks decreasing block sizes from the largest t-test statistics down till the null is not rejected.

Sample split analysis

If `sample split analysis' is on, the significance of every variable in the final model is tested in two overlapping sub-samples. The variables are penalized accordingly and reliability statistics are recorded.

Sample-size adjusted significance level

If `sample-size adjustment' is on, the significance levels change with the sample size.

Note: Sample-size adjustment is only provided for the built-in strategies.

Modelling strategies

Liberal strategy: Built-in PcGets strategy focussing on the control of the non-selection probability of relevant variables.
Conservative strategy: Built-in PcGets strategy focussing on the control of the non-deletion probability of nuisance variables.
Expert user's strategy: Strategy as defined in Options.

Reporting

Report only the finally selected model

Prints the GUM and the selected model.

Write each iteration (condensed)

Prints major steps of the model reduction.

symbol	Reduction path information
`.`	single reduction step: a variable or group of variables has been removed;
`*`	reduction failed, path returns to the previous specification;
`f`	reduction failed, path is not continued.
`c`	reduction path converged to a previously found reduction;
`t`	terminal specification found.

Write each iteration (detailed)

Prints every step with detailed information.

Note: The setting is only relevant for GETS/GETSIVE.

Model estimation

The following information is needed to estimate an equation:

The model formulation;
The initial and final observation of the sample;
The number of forecasts to be withheld for testing parameter constancy;
The method of estimation:

PcGets will elicit information on all these aspects. Models may be revised interactively after formulation and after estimation.

Estimate Model dialog box

The Estimate command provides Dynamic Model Estimation.

Select an estimation method, sample period, and number of forecasts for the formulated model.

The Method Options

Ordinary Least Squares Estimation (OLS)
Testimation (GETS)
Instrumental Variables Estimation (IVE)
Instrumental Variables Testimation (GETSIVE)
Estimation sample: Enter the sample period you wish to use for the estimation (including initialization and forecasts), e.g. 1960 1 to 1980 4. The maximum sample is given one line up.
The default is the sample of the previous estimation (of course only if possible). PcGets automatically excludes observations with missing values.
Less forecasts: Enter the number of observations you wish to withhold for forecasting.
Options: Allows setting the estimation options.
OK: Pressing OK starts the estimation, unless there still is something missing or wrong in the dialog.

Ordinary Least Squares Estimation (OLS)

Ordinary Least Squares is the standard textbook method. OLS is valid if the data model is congruent.

Congruency

The requirements for congruency are:

Homoscedastic innovation errors;
Weakly exogenous regressors;
Constant parameters;
Theory consistency;
Data admissibility;
Encompassing rival models.

PcGets provides tests of most of the aspects of model congruency.

Testimation (GETS)

GETS (general-to-specific) offers a computer-automated model selection when the precise formulation of an econometric relationship is not known a priori.

Starting from a general model which is congruent with the data evidence, statistically-insignificant variables are eliminated, with diagnostic tests checking the validity of reductions, to ensure a congruent final selection.

Instrumental Variables Estimation (IVE)

A structural representation is parsimonious with parameters but has regressors which are correlated with the error term. IVE requires that the reduced form is a congruent data model. The Instrumental variables are the reduced form regressors. Instrumental Variables include two stage least squares (2SLS) as a special case.

PcGets needs to know the status of the variables in the model:
1. At least one endogenous variable on the right-hand side;
2. At least as many instruments as endogenous rhs variables.

Instrumental Variables Testimation (GETSIVE)

GETSIVE operates like GETS but using Instrumental Variables methods instead of Ordinary Least Squares.

Options (Expert user's strategy)

Options allows to specify an expert user strategy. It referes to settings which are changed infrequently, and are persistent between runs of PcGets.

Significance levels

t - tests: Sets the significance level of t-tests.
F - tests: Sets the significance level of F-tests.
F - test of the GUM: Sets the significance level of the F-test of the GUM.
Encompassing test: Sets the significance level of the encompassing tests.
Diagnostics (high): Sets the significance level of diagnostic tests (high).
Diagnostics (low): Sets the significance level of diagnostic tests (low).

F presearch tests

F - tests (lag preselection): Sets the significance level of the lag preselection.
F - tests (step 1): Sets the significance level of the top-down reduction presearch (Step 1).
F - tests (step 2): Sets the significance level of the top-down reduction presearch (Step 2).
F - tests (bottom-up): Sets the significance level of the bottom-up reduction presearch.
Marginal t-prob (step 1): Sets the marginal t-prob of the top-down reduction presearch (Step 1).
Marginal t-prob (step 2): Sets the marginal t-prob of the top-down reduction presearch (Step 2).
Marginal t-prob (bottom-up): Sets the marginal t-prob of the bottom-up reduction presearch.
Two-step presearch testing: If checked, the top-down reduction presearch runs through two steps.

Block search

Check groups with t-probs > 0.90: If checked, a reduction path starts by removing a group of variables with t-probs > 0.90.
Check groups with t-probs > 0.70: If checked, a reduction path starts by removing a group of variables with t-probs > 0.70.
Check groups with t-probs > 0.50: If checked, a reduction path starts by removing a group of variables with t-probs > 0.50.
Check groups with t-probs > 0.25: If checked, a reduction path starts by removing a group of variables with t-probs > 0.25.
Check groups with t-probs > 0.10: If checked, a reduction path starts by removing a group of variables with t-probs > 0.10.
Check groups with t-probs > 0.05: If checked, a reduction path starts by removing a group of variables with t-probs > 0.05.
Check groups with t-probs > 0.01: If checked, a reduction path starts by removing a group of variables with t-probs > 0.01.
Check groups with t-probs > 0.001: If checked, a reduction path starts by removing a group of variables with t-probs > 0.001.

Information criterion

AIC: If checked, AIC is used in selecting the specific from the set of final models.
HQ: If checked, HQ is used in selecting the specific from the set of final models.
SC: If checked, SC is used in selecting the specific from the set of final models.
HK: If checked, HK is used in selecting the specific from the set of final models.

Sample split analysis

Significance level: Sets significance level for t-tests in subsamples.
Size of the subsample (fraction): Sets size of the subsample as fraction of the full sample.
Penalty for failed t-test in full sample: Sets penalty for failed t-test in full sample.
Penalty for failed t-test in subsample 1: Sets penalty for failed t-test in subsample 1.
Penalty for failed t-test in subsample 2: Sets penalty for failed t-test in subsample 2.

Outlier detection

Size of marginal outlier (in std.dev.): Determines the size of a marginal outlier (as multiple of s).

Diagnostic tests

Chow test 1: If checked, first Chow test is included in the test battery.
Chow test 2: If checked, second Chow test is included in the test battery.
Portmanteau: If checked, portmanteau statistic is included in the test battery.
Normality: If checked, normality test is included in the test battery.
AR test: If checked, LM test for residual autocorrelation is included in the test battery.
ARCH test: If checked, test for ARCH effects in the residuals is included in the test battery.
Hetero test: If checked, LM test for heteroskedasticity is included in the test battery.

Test options

Chow test breakpoint 1: Sets first breakpoint as fraction of the sample.
Chow rest breakpoint 2: Sets second breakpoint as fraction of the sample.
Portmanteau max lag: Sets number of lags for calculating the portmanteau statistic.
AR test min lag: Sets minimal lag of the LM test for residual autocorrelation.
AR test max lag: Sets maximal lag of the LM test for residual autocorrelation.
ARCH test min lag: Sets minimal lag of the test for ARCH effects in the residuals.
ARCH test max lag: Sets miximal lag of the test for ARCH effects in the residuals.

Reset default

Keep current settings: Leaves the expert settings unchanged when selected.
Liberal strategy: Resets the expert settings to the liberal strategy.
Conservative strategy: Resets the expert settings to the conservative strategy.

Progress (Model menu)

The Progress command reports on the progress to date made in the general to specific modelling strategy the Progress dialog box is used to change the default model nesting sequence.

Progress dialog box

Use this dialog to review the progress made to date in the model reduction, when using different GUMs in the general to specific Modelling Strategy.

Models: Already marked are the models that are sequentially nested in an older (i.e. lower in the list) model. However, PcGets might miss a model that could be nested through transformed variables. You can add such models to the nesting chain by marking them in this Multiple-Selection List box.
Moving from top to bottom through the marked models RSS must decrease, the sample period be constant, and the number of explanatory variables go up. Models that don't satisfy this requirement will be deleted.
Find Results: Will exit the dialog and try to locate the output of the highlighted model in the GiveWin results window.
Write batch: Generates batch code with the variables of the GUM, the estimation method and sample and writes it to the Results window.

Progress

The progress report consists of:

Model identification
Number of observations (T)
Number of parameters (p)
Estimation method
Log-Likelihood
Akaike Information Criterion (AIC)
Hannan-Quinn criterion (HQ)
Schwarz Criterion (SC)

Estimation output

Individual equation estimation is allowed by least squares (OLS) and instrumental variables (IVE).

Once a model has been specified, a sample period selected, and an estimation method chosen, the output appears.

Estimated Regression Equation

The first column of these results records the names of the variables and the second, the estimated regression coefficients values. The following three columns give further information about each of the magnitudes described below in 3 to 5.
1. Names of the variables
2. Estimated regression coefficients values
3. Standard Errors of the Regression Coefficients: These are the square roots of the diagonal of the variance-covariance matrix.
4. t-statistics: These statistics are conventionally calculated to determine whether individual coefficients are significantly different from zero (called the null hypothesis, Ho). When Ho is true (and the model is otherwise correctly specified), a Student's t-distribution is used since the sample size is often small and we only have an estimate of the parameter's standard error. However, as the sample size increases, t tends to a standard normal distribution under Ho. Large values of t reject Ho; but, in many situations, Ho may be of little interest to test. Also, selecting variables in a model according to their t values implies that the usual (Neyman-Pearson) justification for testing is not valid.
5. t-probabilities: Gives the probability value of the t-statistic.

Summary regression statistics

Beneath the columnar presentation, an array of summary statistics is provided as follows:
1. Residual Sum of Squares RSS: This is exactly what it states, with s� = RSS/(T-k).
2. Residual standard deviation sigma: This is the standard deviation of the difference between the actual and fitted values in the regression. For a given dependent variable, sigma can be standardized as a percentage of the mean of the original level of the dependent variable y (except when the mean is zero) for comparisons across specifications. Since many economics magnitudes are inherently positive, that standardization is often feasible. If y is in logs, 100s is the percentage standard error.
3. Squared multiple correlation coefficient R²: This is a measure of the goodness of fit of the present regression.
4. Adjusted R² Relative to Difference and Seasonals: This adjusts squared multiple correlation coefficient R² for the loss in the degrees of freedom.
5. Log-Likelihood: Under normality, OLS maximizes the log-likelihood function and is given by log(L) = - T/2 - T/2 log (2p) - 1/2 RSS
6. Akaike Information Criterion (AIC): Information criterion proposed by Akaike (1985), tends to overselect asymptotically. AIC = - 2 log(L)/T + 2 k/T
7. Hannan-Quinn (HQ) criterion: Information criterion proposed by Hannan and Quinn (1979), consistent. HQ = - 2 log(L)/T + 2 k log(log(T))/T
8. Schwarz Criterion (SC): Bayesian information criterion proposed by Schwarz (1978), consistent. SC = - 2 log(L)/T + k log(T)/T These three measures differ in the `penalty' they impose for more parameters where smaller values of all three are preferable, ceteris paribus. From these, other model selection criteria may be calculated. These, and related scalar measures, are often used to choose between alternative models in a class.
9 . Number of observations (T)
10. Number of coefficients (p)
11. FpNull-statistic: The null hypothesis is that the population b vector of the regression coefficients is zero. The probability value for the F-test is reported, calculated using an algorithm based on Majunder and Bhattacharjee (1973a) and Cran, Martin and Thomas (1977).
12. FpConst-statistic: The null hypothesis is that all the regression coefficients except the intercept are zero. The probability value for the F-test is reported.
12*. FpGUM-statistic: Tests the current model reduction against the GUM. The null hypothesis is that all the regression coefficients of the GUM associated with the eliminated variables are zero. The probability value for the F-test is reported.

Diagnostic testing

PcGets controls the validity of model reductioms by diagnostic testing for: white noise vs residual serial correlation constant variance vs residual ARCH normality vs residual non-normality homoscedasticity vs residual heteroscedasticity parameter constancy vs parameter instability Test statistics and marginal rejection probabilities are reported for the following diagnostics:
1. Chow tests: Chow's (1960) test statistic check the parameter constancy of the model: ( [RSS_T+h - RSS_T] / h) / ( RSS_T / [T-k] ) The marginal rejection probability reported assumes an F distribution which is the exact distribution for fixed regressors, but is only approximately (or asymptotically) so in dynamic models.
2. Portmanteau statistic: Statistic based on T*(sum of s squared autocorrelations) with s the length of the correlogram T² S^s_j=1 r_j²/(T-j) Note: Residual correlogram, autoregression and Durbin-Watson test are not valid for models with lagged dependent variables, or only weakly (as opposed to strongly) exogenous variables, whereas the LM test for error autocorrelation (4.) is valid.
3. Normality: The Normality test checks whether the residuals are normally distributed as: u_t ~ IN(0,1) with E[u_t³] = 0, and E[u_t⁴] = 3s². A c² test is reported (with 2 degrees of freedom), and the output includes all moments up to the fourth. The null hypothesis is normality, which will be rejected at the 5% level, if a test statistic of more than 5.99 is observed. The reported test statistic has a small-sample correction.
4. Error autocorrelation: Yields a Lagrange-Multiplier (LM) test for serial correlation: u_t = S^r_i=s r_i u_t-i + e_t for 0 £ s £ r £ 12, with e ~ IID(0,s²). The F-test is performed by an auxiliary regression of the residuals on the original variables and lagged residuals (missing lagged residuals at the start of the sample are replaced by zero, so no observations are lost). The null hypothesis is no autocorrelation, which would be rejected if the test statistic is too high. This LM test is valid for models with lagged dependent variables, whereas neither the DW nor the residual correlogram provide a valid test in that case.
5. Autoregressive Conditional Heteroscedasticity (ARCH): Checks whether the residuals have an ARCH structure: E[ u_t² | u_t-1 , ..., u_t-r ] = S^r_i=s a_i u_t-i², with [0 £ s £ r £ 12] and e ~ IID(0, t²). An F-statistic is reported. The null hypothesis is no ARCH, which would be rejected if the test statistic is too high. This test is done by regressing the squared residuals on a constant and lagged squared residuals (now some observations are lost at the beginning of the sample).
6. Heteroscedasticity: Tests if the u have constant variances against the alternative that u² depends on the original and squared regressors. The null hypothesis is no heteroscedasticity, which would be rejected if the test statistic is too high. The reported F-statistic is derived by an auxiliary regression of the squared residuals on a constant, the original regressors, and the original regressors squared.

Graphic analysis dialog box

The Graphic analysis command gives access to various graphs of actual and fitted values, residuals and visual representations of the properties of the residuals.

Actual and fitted values

1. Actual and fitted values: Shows the fitted and actual values of the dependent variable over time, over the whole sample period, including the forecast period.
2. Cross-plot of actual and fitted: As above, but now a cross-plot of actual and fitted values.
3. Residuals (scaled): Shows the scaled residuals against time over the sample period. The residuals are scaled by the residual standard deviation.
4. Squared residuals (normalized): Shows the squared residuals against time over the sample period, scaled by the residual variance.

Residual analysis

1. Correlogram: Shows the auto correlation function (ACF) and the Partial autocorrelation function (PACF) of the residuals.
2. Residual density and histogram: Density estimate and histogram of the residuals. The normal density with the same mean and variance is drawn for reference.
3. Residual spectrum: Shows the Spectral density of the residuals, using the lag length of the ACF as the truncation point.
4. Residual QQ plot against N(0,1): Plots the ordered residuals in a QQ plot against the normal distribution.

To zoom a graph adjust the area inside GiveWin.

Data density and histogram

Histograms are a way of looking at the sample distributions of statistics. Then, on the basis of the original data, density functions may be interpolated to give a clearer picture of the implied distributional shape: similarly, cumulative distribution functions may be constructed (and compared on-screen to a Cumulative Normal Density).

Non-parametric density estimation

Given observations:

(x₁ ... x_T) from some unknown probability density function f(×), about which little may be known a priori. To estimate that density without imposing too many assumptions about its properties, a non-parametric approach is used in PcGets based on a kernel estimator of f(×).

The Kernel estimator, ¦, of the density f is defined by:

¦(X)=(Nh)^-1K{h^-1(X-x₁) + ... + h^-1(X-x_T)}, where K{.} is the kernel function and h is a 'window width' or smoothing parameter and corresponds to the width of histogram bars. The kernel K used is the Normal or Gaussian kernel. Research suggests that the density estimate is little affected by the choice of kernel, but is largely governed by the choice of window width, h.

Since evaluating ¦(X) directly can be expensive in computer time, a method based on a Fast Fourier Transform is used in PcGets.

The window width in estimating the density, h = CsT^P, is set to minimize the Integrated Mean Square Error for normal densities: P = -0.2 and C = 1.06.

Correlogram (ACF, PACF)

The correlogram or autocorrelation function (ACF) of a variable, or of the residuals of an estimated model, plots the series of correlation coefficients { r_j } between x_t and x_t-j.

The length s of the ACF is chosen by the user, leading to a figure which shows (r₁, r₂, ..., r_s) plotted against (1,2,..., s).

A related statistic is the Portmanteau (also called Box-Pierce or Q-statistic):

T S^s_j=1 r_j².

The partial autocorrelation coefficients correct the autocorrelation for the effects of previous lags. So the first partial autocorrelation coefficient equals the first normal autocorrelation coefficient.

Spectrum

A stationary series can be decomposed in cyclical components with different frequencies and amplitudes. The spectral density gives a graphical representation of this. It is symmetric around 0, and only graphed for [0,p] (the horizontal axis in the PcGets graphs is scaled by p, and given as [0,1]).

The spectral density consists of a weighted sum of the autocorrelations, using the Parzen window as the weighting function. The truncation parameter m can be set (the larger m, the less smooth the spectrum becomes, but the lower the bias).

A white-noise series has a flat spectrum.

Recursive analysis dialog box

The Recursive analysis command generates recursive estimates of the model and graphs the output.

Recursive Analysis

Recursive estimation (backward): Estimation starts with the initial number of observations at the end of the sample and increases the sample size gradually by one.
Recursive estimation (forward): Estimation starts with the initial number of observations at the beginning of the sample and increases the sample size gradually by one.
Sequential estimation (rolling regression): As in the forward recursion, the estimation starts with the initial number of observations at the beginning of the sample. While the estimation window moves forward, the sample size is kept constant.

Options

Initial number of observations

Enter the number of observations you wish to use for initializing the recursive estimation.

Show estimates, t-values and test statistics in separate windows

If the model contains many variables it is recommened to split up the output in three graphics windows:

Beta coefficients (�2*SE)
Beta t-values
Recursive model statistics (RSS, prediction errors, Chow tests)

Recursive estimation

Recursive Least Squares is OLS where coefficients are estimated sequentially and is a powerful tool for investigating parameter constancy.

Recursive Instrumental Variables operates like Recursive Least Squares but using Instrumental Variables methods.

The sample starts from a minimal number of observations N = K variables and statistics are recalculated adding observations one at a time.

The recursive output is analysed graphically.

Recursive analysis output

The graphical output of the recursive analysis option For T observations and m initial values consists of:

Beta coefficients

Beta coefficients (� 2SE) for all variables of the model; the graphs are centred on b with the approximate 95% confidence interval at each observation shown on either side.

Beta t-values

The `t-statistic' = b/SE for any coefficient.

Recursive model statistics

1. Residual Sums of Squares: Showing RSS at each t, based on the OLS/IVE residuals: RSS = S^t_s=1 n_s² where n_s = y_s - x_s'b_t.
2. 1-step residuals (� 2s): Plotting u = y - x'b and twice the equation standard error at each t on either side of zero. This will reveal any model deficiencies.
3. Chow test statistic: Graphing Chow test statistics for a break at each t.
4. Chow test p-value: Showing the marginal rejection probability of the Chow test statistic.

The Chow statistics are only shown in case of forward OLS recursions, owing to endogenous regressors in the case of IVE.

To zoom a graph adjust the area inside GiveWin.

Dynamic analysis

After estimation, the dynamic properties of models of models like (1) as defined in the Dynamic Model Formulation can be analysed.

PcGets produces the following output:

1. Lag structure analysis: Produces a table of lag coefficients for every variable. B₀(L) y_t = c + B₁(L) x_1,t + B₂(L) x_2,t + ... + B_k(L) x_k,t + e_t, t = 1,...,T. (1) where B_i (L) = b_i,0 + b_i,1 L + b_i,2 L² + ... + b_i,n Lⁿ.
2. Static long-run solution: If the roots of B(L) lie outside the unit circle we can rewrite (1) as (forgetting about c and e): y_t = S^k_i=1 H_i (L) x_i,t, where H_i (L)=B_i (L) / B₀(L). (2) If E[x] has remained at a constant level x for long enough, y will reach its long-run solution: E[y] = S^k_i=1 H_i (1) E[x_i], where H_i (1)=B_i (1) / B₀(1). (3) (reported with asymptotic standard errors).
3. Roots of lag polynomials: Reports the eigenvalues of the autoregressive dynamic (inverse of the roots of the autoregressive lag polynomial) and the roots of the distributed lags (if a variable enters the model more than ones).

Forecasting dialog box

PcGets allows you to retain observations to compute forecasts.

Generates dynamic forecasts (the sequence of 1,2,3,... H-step forecasts) optionally with standard error bars, bands or fans (� 2 forecast standard errors).

Forecast horizon

Year, Period: By default, this displays the maximum number of dynamic forecasts. If there are unmodelled variables in the model, forecasting is only possible while data is available. By default, the final date of data base is reported. If there are exogenous variables in the model, forecasting is only possible while data is available.
Dynamic forecasts: Select this to calculate dynamic forecasts (the sequence of 1,2,3,... H-step forecasts). instead of static 1-step forecasts.

Reporting

Table: Write the information (the forecast, its standard error, the actual value, the forecast error and its t-value) to the Results window.
Graphic: Produce graphical representation of the results.
Cumulated: Calculates forecasts for the cumuland of the modelled variable. For example, when a variable is modelled in differences, it produces forecasts of the level of the variable: y_t+h=y_t + S^h_i=1 Dy_t+i The output is normalized to zero at the time when the forecasts are made. Forecast error standard errors will be computed analytically.
Number of pre-forecast observations: By default all observations are included from the pre-forecasting sample.

Options

Type of error bars: None Use error bars Use error bands Use error fans

For OLS/GETS comprehensive h-step ahead forecasts are produced. For IVE/GETSIVE, the results have to be interpreted with caution since there are endogenous regressor variables. If required, PcGets will compute analytical standard errors of dynamic forecasts.

Omitted variables

This tests if some variables of the GUM which have been deleted by PcGets should be re-added to the specific model.

If the GUM is

y = Xb + Zg +v, and the estimated model is y = Xb + u, then the omitted variables test, tests for g_i= 0 in y = Xb + Z_ig_i +w.

The Lagrange Multiplier F-statistic for single and joint tests is reported, and the null hypothesis is rejected when its value is significant.

Note: The tests require GETS/GETSIVE.

Exclusion Restrictions dialog box

Allows you to select explanatory variables and test whether they are jointly significant. A more general form of the test for linear restrictions.

Selection: Mark all the variables you wish to include in the test in this Multiple-Selection List box.

PcGets tests whether the selected variables can be deleted from the model.

Linear Restrictions dialog box

Tests for linear restrictions are specified in the form of a matrix R, and a vector r. These are entered as one matrix [R : r] in the dialog.

For example, if the model is mp on Constant, mp_1, y, y_1, and we wish to test that the coefficients on y and y_1 add up to one, and that on mp_1 equals zero. Then the R:r matrix can be written as

0 1 0 0 0 0 0 1 1 1 The first four columns are the columns of R, specifying two restrictions. The last column is r, which specifies what the restrictions should add up to.

The dimensions of the matrix must be specified in the rows and columns fields. It is your responsibility to specify the right values, PcGets will not try to work it out (because elements of a row may be spread over several lines).

Rows: The number of rows in the matrix.
Columns: The number of columns in the matrix.
Matrix: This window is a basic text editor in which you can edit a matrix file. Here you can enter the R:r matrix as in the above example.
Set to zero: This could be useful to create an initial matrix. Select variables in the model box (this is a this multiple-selection list box). and press this button to specify the R:r matrix which corresponds to the restriction that each selected variable has coefficient zero (so one row for each selected variable)
Load: Enables you to load an existing matrix file into the editor. Any existing matrix in the editor will be lost.
Save: Enables you to save the contents of the editor in an matrix file, so that it can be used again.

Tests for linear restrictions

If we write the model as

y = Xb + u, where y is (T x 1), b is (k x 1) and X is (T x k), then linear restrictions can be expressed in vector form as: Rb = r, where R is a (p x k) matrix, and r a (p x 1) vector.

E.g. the two restrictions: a = 1 and b = -g in

mp = b + a mp₁ + b y + g y₁ can be expressed as: | 0 1 0 0 | R = | |, r' = [0 1]. | 0 0 1 1 |

PcGets allows you to test general linear restrictions by specifying R and r, in the form of a (p x k+1) matrix [R : r]. Simple linear restrictions of the form a =... = d = 0 can be done by selecting the relevant variables.

The null-hypothesis Ho: Rb = r is rejected if we observe a significant test statistic.

Two tests of linear restrictions are routinely reported in PcGets:
1. Ho: b = 0, where the test-statistic is the t-ratio of b.
2. Ho: a = ... = d = 0 (all coefficients apart from the constant are zero).
Shown as the F-statistic which follows R� (and can be derived from it).

Matrix File

A matrix file holds a matrix, preceded by the matrix dimensions.

It will normally have the .MAT extension. Lines starting with ; or // are treated as comments. An example of a matrix file is:

+---------+ � 2 3 � <-- dimensions, a 2 by 3 matrix �//comment� <-- a line of comment � 1 0 0 � <-- first row of the matrix � 0 1 .5 � <-- second row of the matrix +---------+

Reporting

PcGets settings report

Reports the recent settings of PcGets.

LaTeX output

The resulting output can be pasted to a LaTeX document.

PcGets batch (General)

Generates batch code to reestimate the GUM.

PcGets batch (Specific)

Generates batch code to reestimate the Specific.

PcGive batch

Generates batch code to analyze the (specific) model with PcGive.

PcFiml batch

Generates batch code to prepare the system estimation by PcGive.

Store in database (Test menu)

Use the store in database dialog to store residuals or fitted values, or recursive outcomes, etc. in the current database.

Store in database dialog

Allows you to save in the database

Residuals or
Fitted values.

Following tbe sucsessful generation of forecasts, you can also save:

Forecasts.

Following the detection of outliers during GETS/GETSIVE

Dummies.

GiveWin will prompt for a variable name.

List Boxes

A list box shows a list of available choices. Sometimes only one choice can be made, sometimes muliple items can be chosen. In the latter case it is called a Multiple-Selection List box. Scroll bars are provided if not all items fit in the list box.

Select a single item in the list box with one of these procedures:

Use the scroll bar to make the item visible, then click the item.
Double-click to complete.
Use Arrow Up/Arrow Down or Page Up/Page Down to highlight the item.
Typing a lower case letter will highlight the next item starting with that letter.
Press Enter to complete the command.

Multiple-Selection List boxes

A multiple selection list box allows for marking as many items as desired.

With the keyboard it is only possible to mark a single variable (by using the arrow up and down keys), or range of variables (hold the Shift key down while using the arrow up or down keys).

With the mouse there is more flexibility:

single click to select one variable;
hold the left mouse button down to select a range of variables;
hold the Ctrl key down and click to select additional variables;
hold the Shift key down and click to extend the selection range.

Combo Boxes

A combo box is a combination of an edit box, and a list box. You can enter text directly, or selecting from a list.

Activate the list by

Clicking on the arrow down
Pressing Arrow Down.

Missing values

Missing values are set to -9999.99. Such values are not included in any statistical calculations or graphs (where gaps are left), but are displayed when viewing the database.

Only contiguous sequences without missing values are used.

Cross-section data can be sorted to ensure all missing values are collected at the end of the sample, so all other data can be used.

This file last changed .