Time series analysis - lecture 4 Consumer Price Index - Clothing and Footwear.

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Time series analysis - lecture 4 Consumer Price Index - Clothing and Footwear

Time series analysis - lecture 4 Consumer Price Index - Clothing and Footwear

Time series analysis - lecture 4 Seasonally differenced Consumer Price Index - Clothing and Footwear

Time series analysis - lecture 4 Seasonally differenced Consumer Price Index - Clothing and Footwear

Time series analysis - lecture 4 CPI Clothing and Footwear SARIMA (1, 0, 0, 0, 1, 0) Final Estimates of Parameters Type Coef SE Coef T P AR Constant Differencing: 0 regular, 1 seasonal of order 12 Number of observations: Original series 178, after differencing 166 Residuals: SS = (backforecasts excluded) MS = DF = 164

Time series analysis - lecture 4 CPI Clothing and Footwear SARIMA (1, 0, 0, 2, 1, 0) Final Estimates of Parameters Type Coef SE Coef T P AR SAR SAR Constant Differencing: 0 regular, 1 seasonal of order 12 Number of observations: Original series 178, after differencing 166 Residuals: SS = (backforecasts excluded) MS = DF = 162

Time series analysis - lecture 4 CPI Clothing and Footwear SARIMA (1, 0, 0, 2, 1, 0) residuals

Time series analysis - lecture 4 Models for multiple time series of data  Dynamic regression models  General input-output models  Models for intervention analysis  Response surface methodologies  Smoothing of multiple time series  Change-point detection

Time series analysis - lecture 4 Percentage of carbon dioxide in the output from a gas furnace

Time series analysis - lecture 4 The dynamic regression model where Y t = the forecast variable (output series); X t = the explanatory variable (input series); N t = the combined effect of all other factors influencing Y t (the noise); (B) = ( B + 2 B 2 + … + k B k ), where k is the order of the transfer function

Time series analysis - lecture 4 Using the SAS procedure AUTOREG - regression in which the noise is modelled as an autoregressive sequence Consider a dataset with one input variable (gasrate) and one output variable (CO 2 ) data newdata; set mining.gasfurnace; gasrate1= lag1(gasrate); gasrate2= lag2(gasrate); gasrate3=lag3(gasrate); gasrate4= lag4(gasrate); run; proc autoreg data=newdata; model CO2 = gasrate/nlag=1; model CO2 = gasrate gasrate1/nlag=1; model CO2 = gasrate gasrate1 gasrate2/nlag=1; model CO2 = gasrate gasrate1 gasrate 2 gasrate3/nlag=1; model CO2 = gasrate gasrate1 gasrate2 gasrate3 gasrate4/nlag=1; output out=model4 residual=res; run;

Time series analysis - lecture 4 Predicted and observed levels of carbon dioxide in the output from a gas furnace - dynamic regression model with inputs time-lagged up to 4 steps

Time series analysis - lecture 4 No. air passengers by week in Sweden -original series and seasonally differenced data

Time series analysis - lecture 4 Intervention analysis where Y t = the forecast variable (output series); X t = the explanatory variable (step or pulse function); N t = the combined effect of all other factors influencing Y t (the noise); (B) = ( B + 2 B 2 + … + k B k ), where k is the order of the transfer function