TIME SERIES FORECASTING. ARIMAX, ARCH AND GARCH MODELS FOR UNIVARIATE TIME SERIES ANALYSIS. Examples with Matlab

By B. NORIEGA

This book develops the time series univariate models through the Econometric Modeler tool. This tool allows to work the phases of identification, estimation and diagnosis of a time series. Incorporates AR, MA, ARMA, ARIMA, ARCH, GARCH and ARIMAX models. The Econometric Modeler app is an interactive tool for analyzing univariate time series data. The app is well suited for visualizing and transforming data, performing statistical specification and model identification tests, fittingmodels to data, and iterating among these actions. When you are satisfied with a model, you can export it to the MATLAB Workspace to forecast future responses or for further analysis. You can also generate code or a report from a session.

• Language: English
• Publisher: Lulu.com
• Release date: Jan 15, 2023
• ISBN: 9781447887317

Book preview

TIME SERIES FORECASTING. ARIMAX, ARCH AND GARCH MODELS FOR UNIVARIATE TIME SERIES ANALYSIS

Examples with Matlab

B. NORIEGA

ARIMAX/GARCH MODELS WITH ECONOMETRIC MODELER

This book develops the time series univariate models through the Econometric Modeler tool. This tool allows to work the phases of identification, estimation and diagnosis of a time series. Incorporates AR, MA, ARMA, ARIMA, ARCH, GARCH and ARIMAX models.

The Econometric Modeler app is an interactive tool for analyzing univariate time series data. The app is well suited for visualizing and transforming data, performing statistical specification and model identification tests, fittingmodels to data, and iterating among these actions. When you are satisfied with a model, you can export it to the MATLAB Workspace to forecast future responses or for further analysis. You can also generate code or a report from a session.

Start Econometric Modeler by entering econometricModeler at the MATLAB command line, or by clicking Econometric Modeler under Computational Finance in the apps gallery (Apps tab on the MATLAB Toolstrip). The following workflow describes how to find a model with the best in-sample fit to time series data using Econometric Modeler. The workflow is not a strict prescription—the steps you implement depend on your goals and the model type. You can easily skip steps and iterate several steps as needed. The app is well suited to the Box-Jenkins approach to time series model building.

1. Prepare data for Econometric Modeler — Select a response variable to analyze and from which to build a predictive model. Optionally, select explanatory variables to include in the model. You can import only one variable from the MATLAB Workspace into Econometric Modeler. Therefore, at the command line, you must synchronize and concatenate multiple series into one variable.

2. Import time series variables — Import Data into Econometric Modeler from the MATLAB Workspace or a MAT-file. After importing data, you can adjust variable properties or the presence of variables.

3. Perform exploratory data analysis — View the series in various ways, stabilize a series by transforming it, and detect time series properties by performing statistical tests.

• Visualize time series data — Supported plots include time series plots and correlograms (for example, the autocorrelation function (ACF)).

• Perform specificationandmodelidentificationhypothesis tests — Test series for stationarity,heteroscedasticity,autocorrelation, and collinearity among multiple series. For ARIMA and GARCH models, this step can include determining the appropriate number of lags to include in the model. Supported Econometric Modeler App Overview tests include the augmented Dickey-Fuller test, Engle's ARCH test, the Ljung-Box Q-test, and Belsley collinearity diagnostics.

• Transform time series — Supported transformations include the log transformation and seasonal and nonseasonal differencing.

4. Fit candidate models to the data — Choose model parametric forms for a univariate response series based on the exploratory data analysis or dictated by economic theory. Then, estimate the model. Supported models include seasonalandnonseasonalconditional mean (for example, ARIMA), conditional variance (for example, GARCH), and multiple linear regression models (optionally containing ARMA errors).

5. Conduct goodness-of-fit checks — Ensure that the model adequately describes the data by performing residual diagnostics. • Visualize the residuals to check whether they are centered on zero, normally distributed, homoscedastic, and serially uncorrelated. Supported plots include quantile-quantile and ACF plots.

• Test the residuals for homoscedasticity and autocorrelation. Supported tests include the Ljung-Box Q-test and Engle's ARCH test on the squared residuals.

6. Find the model with the best in-sample fit — Estimate multiple models within the same family, and then choose the model that yields the minimal fit statistic, for example, Akaike information criterion (AIC).

7. Export session results — After you find a model or models that perform adequately,summarizetheresults ofthesession.The methodyou choose depends on your goals. Supported methods include:

• Export variables — Econometric Modeler exports selected variables to the MATLAB Workspace. If a session in the app does not complete your análisis goal, such as forecasting responses, then you can export variables (including estimated models) for further analysis at the command line.

• Generate a function — Econometric Modeler generates a MATLAB function that returns a selected model given the imported data. This method helps you understand the command-line functions that the app uses to create predictive models. You can modify the generated function to accomplish your analysis goals.

• Generate a report — Econometric Modeler produces a document, such as, a PDF, describing your activities on selected variables or models. This method provides a clear and convenient summaryof your analysis whenyou completeyour goal in the app.

CONTENTS

Econometric Modeler App Overview

Prepare Data for Econometric Modeler App Import Time Series Variables

Perform Exploratory Data Analysis Fitting Models to Data

Conducting Goodness-of-Fit Checks Finding Model with Best In-Sample Fit Export Session Results

Specifying Lag Operator Polynomials Interactively Specify Lag Structure Using Lag Order Tab Specify Lag Structure Using Lag Vector Tab

Prepare Time Series Data for Econometric Modeler App Prepare Table of Multivariate Data for Import

Prepare Numeric Vector for Import

Import Time Series Data into Econometric Modeler App Import Data from MATLAB Workspace

Import Data from MAT-File

Plot Time Series Data Using Econometric Modeler App Plot Univariate Time Series Data

Plot Multivariate Time Series and Correlations

Detect Serial Correlation Using Econometric Modeler App Plot ACF and PACF

Conduct Ljung-Box Q-Test for Significant Autocorrelation

Detect ARCH Effects Using Econometric Modeler App Inspect Correlograms of Squared Residuals for ARCH Effect

s

Conduct Ljung-Box Q-Test on Squared Residuals Conduct Engle's ARCH Test

Assess Stationarity of Time Series Using Econometric Modeler

Test Assuming Unit Root Null Model Test Assuming Stationary Null Model

Test Assuming Random Walk Null Model

Assess Collinearity Among Multiple Series Using Econometric Modeler App

Transform Time Series Using Econometric Modeler App Apply Log Transformation to Data

Stabilize Time Series Using Nonseasonal Differencing Convert Prices to Returns

Remove Seasonal Trend from Time Series Using Seasonal Differ ence

Remove Deterministic Trend from Time Series

Implement Box-Jenkins Model Selection and Estimation Using Econometric Modeler App

Select ARCH Lags for GARCH Model Using Econometric Modeler App

Estimate Multiplicative ARIMA Model Using Econometric Modeler App

Perform ARIMA Model Residual Diagnostics Using Econometric Modeler App

Specify t Innovation Distribution Using Econometric Modeler App

Compare Predictive Performance After Creating Models Using Econometric Modeler App

Estimate ARIMAX Model Using Econometric Modeler App

Estimate Regression Model with ARMA Errors Using Econometric Modeler App

Compare Conditional Variance Model Fit Statistics Using Econometric Modeler App

Perform GARCH Model Residual Diagnostics Using Econometric Modeler App

Share Results of Econometric Modeler App Session

Econometric Modeler

• Econometric Modeler App Overview

• Specifying Lag Operator Polynomials Interactively

• Prepare Time Series Data for Econometric Modeler App • Import Time Series Data into Econometric Modeler App • Plot Time Series Data Using Econometric Modeler App

• Detect Serial Correlation Using Econometric Modeler App • Detect ARCH Effects Using Econometric Modeler App

• Assess Stationarity of Time Series Using Econometric Modeler

• Assess Collinearity Among Multiple Series Using Econometric Modeler App • Transform Time Series Using Econometric Modeler App

• Implement Box-Jenkins Model Selection and Estimation Using Econometric Modeler App

• Select ARCH Lags for GARCH Model Using Econometric Modeler App • Estimate Multiplicative ARIMA Model Using Econometric Modeler App

• Perform ARIMA Model Residual Diagnostics Using Econometric Modeler App • Specify t Innovation Distribution Using Econometric Modeler App

• Compare Predictive Performance After Creating Models Using Econometric Modeler App

• Estimate ARIMAX Model Using Econometric Modeler App

• Estimate Regression Model with ARMA Errors Using Econometric Modeler App

• Compare Conditional Variance Model Fit Statistics Using Econometric Modeler App • Perform GARCH Model Residual Diagnostics Using Econometric Modeler App

Econometric Modeler App Overview

The Econometric Modeler app is an interactive tool for analyzing univariate time series data. The app is well suited for visualizing and transforming data, performing statistical specification and model identification tests, fitting models to data, and iterating among these actions. When you are satisfied with a model, you can export it to the MATLAB Workspace to forecast future responses or for further analysis. You can also generate code or a report from a session.

Start Econometric Modeler by entering econometricModeler at the MATLAB command line, or by clicking Econometric Modeler under Computational Finance in the apps gallery (Apps tab on the MATLAB Toolstrip).

The following workflow describes how to find a model with the best in-sample fit to time series data using Econometric Modeler. The workflow is not a strict prescription—the steps you implement depend on your goals and the model type. You can easily