SMOOTHING PARAMETER JMP 9 GRAPH BUILDER SERIES

Moving average model described above has the undesirable property that it Simple Exponential Smoothing (exponentially weighted moving average) You could then compute the sample standard deviations of the errors at eachįorecast horizon, and then construct confidence intervals for longer-termįorecasts by adding and subtracting multiples of the appropriate standard ForĮxample, you could set up a spreadsheet in which the SMA model would be used toįorecast 2 steps ahead, 3 steps ahead, etc., within the historical data sample. Statistical theory that tells us how the confidence intervals ought to widenĮstimates of the confidence limits for the longer-horizon forecasts. This is obviously not correct! Unfortunately, there is no underlying Moving average do not get wider as the forecasting horizon increases. Limits computed by Statgraphics for the long-term forecasts of the simple

However, whereas the forecasts from the random walk model are simplyĮqual to the last observed value, the forecasts from the SMA model are equal to Thus, the SMA model assumes that there is no trend in To the data, i.e., the smallest forecast errors on average.įrom the SMA model are a horizontal straight line, just as in the Is customary to adjust the value of k in order to obtain the best 'fit' As with any parameter of a forecasting model, it (comparable to the length of the estimation period), the SMA model isĮquivalent to the mean model. Note that if m=1, the simple moving average (SMA) model isĮquivalent to the random walk model (without growth). 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

SMOOTHING PARAMETER JMP 9 GRAPH BUILDER SERIES

“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)

Smoothing parameter jmp 9 graph builder