Forecasting based on creeping trend with harmonic weights基于蠕动趋势与谐波量预测.ppt

Forecasting based on creeping trend with harmonic weights Creeping trend can be used if variable changes irregularly in time. We use OLS to estimate parameters of partial trends. Step I Determine the smoothing constant 1kn. The most often used k=3. The quality of smoothing depends on the smoothing constant. How to select the smoothing constant? Let’s have a look at your data. Detect the first turning point. turning point Step I cont. If great variation in a short time can be observed, small value of smoothing constant need to be selected. If small variation in a short time can be observed, great value of smoothing constant may be selected. Greater value of smoothing constant causes greater smoothing of data (with great values of smoothing constant, time series data react slowly to any changes that may occur). Step II Estimation of parameters with OLS for partial trends (smoothing constant, k, is the number of cases for each partial trend). Step III Determine smoothed values , (fitted values). For a given t from 2 to n-1, there is a set of approximants calculated from the partial trend equation. Step IV Determine mean smoothed value for t. Mean smoothed value is the mean of smoothed values for time period t. Step V Determine trend growth for mean smoothed values Step VI Give weight for trend growth. Weights are in ascending order – this way the newest information are the most important. Weight must sum up to 1. formula for calculating weights: Step VI cont. (weight can be found in statistical tables of harmonic weights if the number of growths is settled). Step VII Determine mean trend growth as the weighted average of trend growth with harmonic weights. Step VIII Forecast for time period T Step IX Confidence interval for forecast requires calculating uT Step IX cont. uα depends on normality of residuals. If we didn’t reject the null hypothesis (residuals distribution is roughly normal), and n30 u can be found in norm