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The observed values of the time series;\cf2 \par PERIOD = Wnt01 Spr01 Sum01; \par X = 2800 2925 3040; \par \par \cf3 ! Initialization for zeroth period;\cf2 \par SZ= 2950; \par \cf3 ! To disable the trend, set TZ = BETA = 0;\cf2 \par TZ = 0; \par \cf3 ! How many periods we forecast ahead;\cf2 \par LEAD = 1; \cf3 ! Must be <= number of seasons;\cf2 \par \cf3 ! The smoothing constants;\cf2 \par ALPHA = .1; \par BETA = 0; \par GAMMA = .2; \par \par \cf1 ENDDATA\cf2 \par \cf3 ! Number of periods in a season;\cf2 \par NSEAS = \cf1 @SIZE\cf2 ( SEASON); \par \cf3 ! Number of periods;\cf2 \par NPER = \cf1 @SIZE\cf2 ( PERIOD); \par \par \cf3 ! Update for first period, \par the base;\cf2 \par S( 1) = ALPHA * X( 1)/ MZ( 1) + \par ( 1 - ALPHA) * ( SZ + TZ); \par \cf3 ! Update seasonal factor estimate;\cf2 \par I( 1) = GAMMA * X( 1)/ S( 1) + \par (1 - GAMMA) * MZ( 1); \par \cf3 ! Update B estimate;\cf2 \par B( 1) = BETA * ( S( 1) - SZ) + \par ( 1 - BETA) * TZ; \par \par \cf3 ! Updates for initial cycle;\cf2 \par \cf1 @FOR\cf2 ( PERIOD( T) | T #GT# 1 #AND# T #LE# NSEAS: \par \cf3 ! The base;\cf2 \par S( T) = ALPHA * X( T)/ MZ( T) + \par ( 1 - ALPHA) * ( S( T - 1) + B( T - 1)); \par \cf3 ! Update seasonal factor estimate;\cf2 \par I( T) = GAMMA * X( T)/ S( T) + \par (1 - GAMMA) * MZ( T); \par \cf3 ! Update trend estimate;\cf2 \par B( T) = BETA * ( S( T) - S( T - 1)) + \par ( 1 - BETA) * B( T - 1); \par ); \par \par \cf3 ! For general period;\cf2 \par \cf1 @FOR\cf2 ( PERIOD( T) | T #GT# NSEAS: \par \cf3 ! Calculate the smoothed average based on T observations;\cf2 \par S( T) = ALPHA * X( T)/ I( T - NSEAS) + \par (1 - ALPHA) * ( S( T - 1) + B( T - 1)); \par \cf3 ! Update seasonal factor estimate;\cf2 \par I( T) = GAMMA * X( T)/ S( T) + \par (1 - GAMMA) * I( T - NSEAS); \par \cf3 ! Update B estimate;\cf2 \par B( T) = BETA * ( S( T) - S( T - 1)) + \par ( 1 - BETA) * B( T - 1); \par ); \par \par \cf3 ! Calculate forecast for period T + LEAD;\cf2 \par \cf1 @FOR\cf2 ( PERIOD( T)| T + LEAD #LE# NSEAS: \par F( T) = \par ( S( T) + B( T) * LEAD) * MZ( T + LEAD ) \par ); \par \cf1 @FOR\cf2 ( PERIOD( T)| T + LEAD #GT# NSEAS: \par F( T) = \par ( S( T) + B( T) * LEAD) * I( T + LEAD - NSEAS) \par ); \par \par \cf3 ! Calculate forecast errors;\cf2 \par \cf1 @FOR\cf2 ( PERIOD( T)| T + LEAD #LE# NPER: \par ERRU( T) - ERRD( T) = F( T) - X( T + LEAD); \par ); \par \par \cf3 ! The following is relevant if we are optimizing \par the choice of ALPHA and BETA;\cf2 \par \cf3 ! The degree of the objective. N may be changed \par to 1 to minimize absolute deviation;\cf2 \par N = 2; \par \par \cf3 ! The objective function;\cf2 \par [OBJ] \cf1 MIN\cf2 = \cf1 @SUM\cf2 ( PERIOD: ERRU ^ N + ERRD ^ N); \par \cf3 ! Turn these on if optimizing ALPHA, BETA, and GAMMA;\cf2 \par \cf3 ! Exclude risky weights near zero or one;\cf2 \par \cf3 ! @BND(.01, ALPHA,.99);\cf2 \par \cf3 ! @BND(.01, BETA, .99);\cf2 \par \cf3 ! @BND(.01, GAMMA, .99);\cf2 \par \par \cf3 ! A copy of LINGO can be downloaded from: \par http://www.lindo.com;\cf2 \par \cf1 END\cf2 \par \par }