Regression Analysis and Forecasting Models
A forecast is merely a prediction about the future values of data. However, most extrapolative model forecasts assume that the past is a proxy for the future. That is, the economic data for the 2012–2020 period will be driven by the same variables as was the case for the 2000–2011 period, or the 2007–2011 period. There are many traditional models for forecasting: exponential smoothing, regression, time series, and composite model forecasts, often involving expert forecasts. Regression analysis is a statistical technique to analyze quantitative data to estimate model parameters and make forecasts. We introduce the reader to regression analysis in this chapter.
The horizontal line is called the X-axis and the vertical line the Y-axis. Regression analysis looks for a relationship between the X variable (sometimes called the “independent” or “explanatory” variable) and the Y variable (the “dependent” variable).
For example, X might be the aggregate level of personal disposable income in the United States and Y would represent personal consumption expenditures in the United States, an example used in Guerard and Schwartz (2007). By looking up these numbers for a number of years in the past, we can plot points on the graph. More speciﬁcally, regression analysis seeks to ﬁnd the “line of best ﬁt” through the points. Basically, the regression line is drawn to best approximate the relationship J.B. Guerard, Jr., Introduction to Financial Forecasting in Investment Analysis, DOI 10.1007/978-1-4614-5239-3_2, # Springer Science+Business Media New York 2013
2 Regression Analysis and Forecasting Models
between the two variables. Techniques for estimating the regression line (i.e., its intercept on the Y-axis and its slope) are the subject of this chapter. Forecasts using the regression line assume that the relationship which existed in the past between the two variables will continue to exist in the future. There may be times when this assumption is inappropriate, such as the “Great Recession” of 2008 when the housing market bubble burst. The forecaster must be aware of this potential pitfall. Once the regression line has been estimated, the forecaster must provide an estimate of the future level of the independent variable. The reader clearly sees that the forecast of the independent variable is paramount to an accurate forecast of the dependent variable.
Regression analysis can be expanded to include more than one independent variable. Regressions involving more than one independent variable are referred to as multiple regression. For example, the forecaster might believe that the number of cars sold depends not only on personal disposable income but also on the level of interest rates. Historical data on these three variables must be obtained and a plane of best ﬁt estimated. Given an estimate of the future level of personal disposable income and interest rates, one can make a forecast of car sales. Regression capabilities are found in a wide variety of software packages and hence are available to anyone with a microcomputer. Microsoft Excel, a popular spreadsheet package, SAS, SCA, RATS, and EViews can do simple or multiple regressions. Many statistics packages can do not only regressions but also other quantitative techniques such as those discussed in Chapter 3 (Time Series Analysis and Forecasting). In simple regression analysis, one seeks to measure the statistical association between two variables, X and Y. Regression analysis is generally used to measure how changes in the independent variable, X, inﬂuence changes in the dependent variable, Y. Regression analysis shows a statistical association or correlation among variables, rather than a causal relationship among variables. The case of simple, linear, least squares regression may be written in the form Y ¼ a þ bX þ e;
where Y, the dependent variable, is a linear function of X, the...
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