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Time Series Forecasting


In this chapter we have discussed using univariate time series models to forecast future time series values. We began by seeing that it can be useful to think of a time series as consisting of trend, seasonal, cyclical, and irregular components. If these components remain constant over time, then it is appropriate to describe and forecast the time series by using a time series regression model. We discussed using such models to describe no trend, a linear trend, a quadratic trend, and constant seasonal variation (by utilizing dummy variables). We also considered various transformations that transform increasing seasonal variation into constant seasonal variation, and we saw that we can use the Durbin-Watson test to check for first-order autocorrelations. As an alternative to using a transformation and dummy variables to model increasing seasonal variation, we can use the multiplicative decomposition method. We discussed this intuitive method and saw how to calculate approximate prediction intervals when using it. We then turned to a consideration of exponential smoothing, which is appropriate to use if the components of a time series may be changing slowly over time. Specifically, we discussed simple exponential smoothing, Holt-Winters' double exponential smoothing, and multiplicative Winters' method. We next considered how to compare forecasting methods by using the mean absolute deviation (MAD) and the mean squared deviation (MSD). We concluded this chapter by showing how to use index numbers to describe time-related data.











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