ARIMA Models in Stata
Learn how to estimate ARIMA models in Stata
ARIMA (Autoregressive Integrated Moving Average) models are a powerful forecasting technique used in time series analysis. In this article, we will discuss the applications of ARIMA models in Stata software and provide a step-by-step video tutorial using a real example to forecast future values of the consumer price index.
We will cover the basics of ARIMA models and how they can be applied to time series data. Additionally, we will demonstrate how to use Stata to estimate an ARIMA model and generate forecasts for future values.
To replicate the content in the tutorial, we have provided a dataset that you can download. Additionally, we offer the material used in the video, including slides and a Stata DO file, which you can purchase for further study and reference.
By the end of this article and video tutorial, you will have a better understanding of ARIMA models and how to apply them to real-world data using Stata software.
What are ARIMA Models?
ARIMA (Autoregressive Integrated Moving Average) models are a powerful tool in time series analysis and forecasting. They combine three components - autoregressive (AR), moving average (MA), and differencing (I) - to model the past values of a time series and predict future values.
The AR component of an ARIMA model looks at the correlation between the current value of a time series and its past values. The MA component examines the errors of the model's past predictions. Finally, the I component is used to ensure the time series is stationary by taking differences between consecutive observations.
ARIMA models can be specified as ARIMA(p,d,q), where p, d, and q are the orders of the AR, I, and MA components respectively. The model can be estimated using various methods, such as maximum likelihood estimation, least squares, or conditional sum of squares. Once the model is estimated, it can be used to forecast future values and analyze the properties of the time series.
ARIMA models are widely used in finance, economics to forecast economic indicators. ARIMA models are commonly used to forecast economic indicators such as GDP, inflation, and employment. By analyzing past data, economists can use ARIMA models to predict future values of these indicators.
Steps to estimate ARIMA Models
Stationarity Testing: The first step in identifying an ARIMA model is to check whether the time series data is stationary or not. A stationary time series has a constant mean and variance over time, and the autocorrelation function (ACF) does not depend on time. There are different methods to test for stationarity such as the Augmented Dickey-Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test.
Identification of Autoregressive (AR) and Moving Average (MA) orders: The second step involves identifying the orders of the AR and MA components in the model. This can be done by analyzing the ACF and partial autocorrelation function (PACF) plots of the stationary time series. The PACF plot shows the correlation between observations at different lags after removing the effects of shorter lags, while the ACF plot shows the correlation between observations at different lags without any removal of the effects of shorter lags.
Estimation of Parameters and Model Selection: The final step is to estimate the parameters of the ARIMA model and select the best model based on statistical criteria such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC). The best model is the one with the lowest AIC or BIC value.
The Box Jenkins Methodology
The Box-Jenkins methodology, developed by George Box and Gwilym Jenkins in the 1970s, is a systematic approach to time series analysis and forecasting. It involves a three-stage process: model identification, model estimation, and model diagnostic checking.
The first stage of the methodology involves identifying an appropriate ARIMA model that best fits the time series data. This involves analyzing the autocorrelation and partial autocorrelation plots and testing for stationarity. In the second stage, the model parameters are estimated using maximum likelihood estimation or other methods. Finally, the estimated model is checked for inadequacies and violations of assumptions by analyzing the residuals of the model and testing for serial correlation, normality, and constant variance
Watch the Video Tutorials
ARIMA Models in Stata Part 1
In this video, we cover the 1st stage of the Box Jenkins Methodology: Identification
ARIMA Models in Stata Part 2
In this video, we cover the 2nd stage of the Box Jenkins Methodology: Estimation
ARIMA Models in Stata Part 3
In this video, we cover the 3rd stage of the Box Jenkins Methodology: Forecasting
Recommended literature
"Time Series Analysis, Forecasting and Control" by Box and Jenkins (1970) - This comprehensive book offers a thorough introduction to time series analysis, with a focus on the Box-Jenkins methodology. It covers everything from data pre-processing to model selection, estimation, and diagnostics. With numerous practical examples and exercises, it's a great resource for both beginners and experienced practitioners.
"Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time" by Pierce and Box (1970) - This seminal paper explores the distribution of residual autocorrelations in ARIMA time series models, and introduces the notion of the "partial autocorrelation function". It's a must-read for anyone interested in the theoretical underpinnings of time series analysis.
"On a Measure of Lack of Fit in Time Series Models" by Ljung-Box (1978) - This classic paper presents the Ljung-Box test, a widely-used statistical test for checking the goodness-of-fit of time series models. It's a concise and accessible introduction to this important topic, with practical examples and insights into the theory behind the test.
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