Last 5 values, the forecasts will be about 3 periods late in responding to Moving average is (m+1)/2 relative to the period for which the forecast isĬomputed: this is the amount of time by which forecasts will tend to lagīehind turning points in the data. Thus, we say the average age of the data in the simple Value of the local mean by about (m+1)/2 periods. Implies that the estimate of the local mean will tend to lag behind the true “Y-hat” to stand for a forecast of the time series Y made at theĮarliest possible prior date by a given model.) This average is centered at period t-(m+1)/2, which (Here and elsewhere I will use the symbol The simplest kind of averagingįor the value of Y at time t+1 that is made at time t equals the simple average Performance of the mean and random walk models. By adjusting the degree of smoothing (the width of the movingĪverage), we can hope to strike some kind of optimal balance between the The same strategy can be used to estimate andĪverage is often called a "smoothed" version of the original seriesīecause short-term averaging has the effect of smoothing out the bumps in the ThisĬan be considered as a compromise between the mean model and the Value of the mean and then use that as the forecast for the near future. Hence, we take a moving (local) average to estimate the current Models is that the time series is locally stationary with a slowly varying The basic assumption behind averaging and smoothing Nonseasonal patterns and trends can be extrapolated using a moving-average Step in moving beyond mean models, random walk models, and linear trend models, Holt’s linear exponential smoothing model Spreadsheet implementation of seasonal adjustment andįor the smoothing models (SAS web site) Moving average andīrown’s simple exponential smoothing modelīrown’s linear exponential smoothing model On inflation and seasonal adjustment and Winters seasonal exponential smoothing On forecasting with moving averages (pdf)
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