Models for Time Series and Forecasting ppt课件内容预览：Describe the trend,cyclical,seasonal,and irregular components of the time series model.Fit a linear or quadratic trend equation to a time series.Smooth a time series with the centered moving average and exponential smoothing techniques.Determine seasonal indexes and use them to compensate for the seasonal effects in a time series.Use the trend extrapolation and exponential smoothing forecast methods to estimate a future value.Use MAD and MSE criteria to compare how well equations fit data.Use index numbers to compare business or economic measures over time.Chapter 18- KeyTermsTime seriesClassical time series modelTrend valueCyclical componentSeasonal componentIrregular componentTrend equationMoving averagepptExponential smoothingSeasonal indexRatio to moving average methodDeseasonalizingMAD criterionMSE criterionConstructing an index using theCPIShifting the base of an indexClassical Time SeriesModelTrendEquationsLinear:=b0+b1xQuadratic:=b0+b1x +b2x2=the trend line estimate of yx =time periodb0,b1,and b2are coefficients that are selected to minimize the deviations between the trend estimates and the actual data values y for the past time periods. Regression methods are used to determine the best values for the coefficients.SmoothingTechniquesSmoothing techniques -dampen the impacts of fluctuation in a time series,thereby providing a better view of the trend and (possibly)the cyclical components.Moving average -a technique that replaces a data value with the average of that data value and neighboring data values.Exponential smoothing -a technique that replaces a data value with a weighted average of the actual data value and the value resulting from exponential smoothing for the previous time period.MovingAverageA moving average for a time period is the average of N consecutive data values,including the data value for that time period.A centered moving average is a moving average such that the time period is at the center of the N time periods used to determine which values to average.If N is an even number,the techniques need to be adjusted to place the time period at the center of the averaged values. The number of time periods N is usually based on the number of periods in a seasonal cycle. The larger N is,the more fluctuation will be smoothed out.Moving Average - AnExampleTime Period DataValue1997, QuarterI8181997, QuarterII8611997, QuarterIII8441997, QuarterIV9061998, QuarterI8671998, QuarterII8993-Quarter Centered Moving Average for 1997, QuarterIV:4-Quarter Centered Moving Average for 1997, QuarterIV:ExponentialSmoothingExponential Smoothing - AnExampleData Smoothed ValueSmoothedValuePeriod Value (a =0.2)(a =0.8)18188188182861826.6852.43844830.1845.74906845.3893.9Calculation for smoothed value for Period 2(a =0.2):E2=a y +(1– a )E1=0.2(861)+0.8(818)=826.62SeasonalIndexesA seasonal index is a factor that adjusts a trend value to compensate for typical seasonal fluctuation in that period of a seasonal cycle.
课件关键字：models for time series and for