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Model Span (n°of obs.) Method PRE-ADJUSTMENT Transformation Mean Correction Correction for Trading Day Effects Correction for Easter Effects Correction for Outliers Critical t-value LS Q1.2009 t-value Corr. for Missing Obs. Corr. for Other Regr. Effects Specif. Of the ARIMA model Non-seas. MA (lag 1) value Non-seas. MA (lag 1) t-value Seasonal MA (lag 4) value Seasonal MA (lag 4) t-value Method of Estimation DECOMPOSITION Arima decomposition Seasonality Information on Diagnostics SA quality index (stand. to 10) STATISTICS ON RESIDUALS Ljung-Box on residuals Box-Pierce on residuals Ljung-Box on squared residuals Box-Pierce on squared residuals DESCRIPTION OF RESIDUALS Normality Skewness Kurtosis OUTLIERS Percentage of outliers Q4.1999 – Q2.2011 (47) Q4.1999 – Q2.2011 (47) Tramo/Seats Logarithm None None None Autom.:AO,LS,TC; 1 Outlier fixed 3.000 -3.78 [-3.000, 3.000] crit.val. 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Model Span (n°of obs.) Method PRE-ADJUSTMENT Transformation Mean Correction Correction for Trading Day Effects Correction for Easter Effects Correction for Outliers Critical t-value Corr. for Missing Obs. Corr. for Other Regr. Effects Specif. Of the ARIMA model Non-seas. MA (lag 1) value Non-seas. MA (lag 1) t-value Seasonal MA (lag 4) value Seasonal MA (lag 4) t-value Method of Estimation DECOMPOSITION Arima decomposition Seasonality Information on Diagnostics SA quality index (stand. to 10) STATISTICS ON RESIDUALS Ljung-Box on residuals Box-Pierce on residuals Ljung-Box on squared residuals Box-Pierce on squared residuals DESCRIPTION OF RESIDUALS Normality Skewness Kurtosis OUTLIERS Percentage of outliers Q4.1999 – Q2.2011 (47) Q4.1999 – Q2.2011 (47) Tramo/Seats Logarithm None None None Autom.:AO,LS,TC 3.000 None None (1 1 0)(0 1 1) (fixed) -0.5338 -3.77 [-2.009, 2.009] 5% -0.9202 -15.24 [-2.009, 2.009] 5% Exact Maximum Likelihood Exact Seasonal model used 2.100 [0, 10] ad-hoc 4.58 [0, 18.30] 5% 0.04 [0, 5.99] 5% 7.62 [0, 18.30] 5% 1.27 [0, 5.99] 5% 4.24 [0, 5.99] 5% -0.65 [-0.74, 0.74] 5% 3.86 [1.52, 4.48] 5% 0.00% [0%, 5.0%] ad-hoc 30 'DOPRGHOORHODERUDWRHGDOODVHULHJUH]]DHVWUDSRODWDGDOO·LQGDJLQHVLqFUHDWR LOVHJXHQWHJUDILFR )DWWXUDWRWRWDOH,QGLFHJUH]]RHGHVWDJLRQDOL]]DWRSHU9LFHQ]D *UH]]D 'HVWDJLRQDOL]]DWD ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, )RQWHHODERUD]LRQHVXGDWL9HQHWR&RQJLXQWXUD ,,, $ GLIIHUHQ]D GHOOD VHULH GHOOD SURGX]LRQH SHU LO IDWWXUDWR WRWDOH QRQ VL q ULWHQXWR QHFHVVDULR O·XWLOL]]R GL RXWOLHUVHGLQROWUHLOPRGHOOR$5,0$XWLOL]]DWRqGLIIHUHQWHGD TXHOORSUHFHGHQWHPHQWHHODERUDWRLQIDWWLQRQVLWUDWWDGLXQPRGHOOR$LUOLQHPDGLXQ PRGHOOR4XLQRQVLVRQRUHJLVWUDWHDQRPDOLHQHLWHVWVWDWLVWLFL 31 'DOULVXOWDWRGL'HPHWUDSRVVRFRQGXUUHLOFRQIURQWRFRQOHDOWUHUHDOWjWHUULWRULDOL )DWWXUDWR7RWDOH,QGLFLGHVWDJLRQDOL]]DWLGHOIDWWXUDWRWRWDOHSHU9LFHQ]D9HQHWRH,WDOLD 9LFHQ]D 9HQHWR ,WDOLD ,,, ,,, ,,, ,,, ,,, ,,, )RQWHHODERUD]LRQHVXGDWL9HQHWR&RQJLXQWXUDH,VWDW ,,, ,,, ,,, ,,, ,,, 'LYHUVDPHQWH GDO JUDILFR GHOOD SURGX]LRQH LQGXVWULDOH TXL VL YHULILFD XQD FHUWD VRPLJOLDQ]D WUD OD VHULH YHQHWD H TXHOOD EHULFD , OLYHOOL GL IDWWXUDWR SHUz VL VWDQQR GLIIHUHQ]LDQGRQHOO·DUFRGHOSULPRVHPHVWUHQHOTXDOHOHD]LHQGHYLFHQWLQHKDQQR UHJLVWUDWR XQD FUHVFLWD PDJJLRUH ULVSHWWR D TXHOOD GHOOD VXD UHJLRQH UDJJLXQJHQGR H VXSHUDQGRFRVuLOLYHOOLUHJLVWUDWLDGLQL]LR,QYHFHSHUO·LQGLFHLWDOLDQRODVWDELOLWj UHJLVWUDWD SHU OD SURGX]LRQH YDOH HVFOXVLYDPHQWH SHU LO SHULRGR SUHFHGHQWH DO SRLFKp GD TXHOO·DQQR q VHJXLWD XQD OHJJHUD FUHVFLWD FUROODWD VXFFHVVLYDPHQWH QHO VHFRQGRVHPHVWUH 32 3HU XQ·DQDOLVL SL DSSURIRQGLWD YLHQH GL VHJXLWR LOOXVWUDWD OD GLQDPLFD GHOOH YDULD]LRQL VXELWHGDOO·LQGLFHGHOIDWWXUDWRWRWDOH )DWWXUDWR7RWDOH9DULD]LRQLFRQJLXQWXUDOLFDOFRODWHVXLQGLFLGHVWDJLRQDOL]]DWLGL9LFHQ]D9HQHWRH,WDOLD 9LFHQ]D 9HQHWR ,WDOLD ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, )RQWHHODERUD]LRQHVXGDWL9HQHWR&RQJLXQWXUDH,VWDW ,,, ,,, 'D TXHVWR JUDILFR VL SXz PHJOLR YHULILFDUH FKH L SULPL DQQL GHO QXRYR PLOOHQQLR VRQR VWDWLPDJJLRUPHQWHSRVLWLYLSHUO·LQGXVWULDYLFHQWLQDFRVDFKHQRQHUDYLVLELOHWUDPLWH LOSUHFHGHQWHJUDILFR ,QROWUHVLSXzIDUHXQDFRQVLGHUD]LRQHVHSHUODSURGX]LRQHLOUHFRUGQHJDWLYRqVWDWR UHJLVWUDWR SHU 9LFHQ]D OR VWHVVR QRQ DFFDGH SHU LO IDWWXUDWR LO TXDOH VHJQD OD VXD SHJJLRU SHUIRUPDQFH QHOO·LQGXVWULD LWDOLDQD &Lz GHY·HVVHUH GRYXWR DOOD FUHVFLWD GHL SUH]]L GL YHQGLWD R GDOOD SRVVLELOH JLDFHQ]D GHL SURGRWWL QHOOH LQGXVWULH GHOODSURYLQFLDYHQHWDFRVDFKHQRQVLqYHULILFDWDQHOUHVWRG·,WDOLD 33 )DWWXUDWRHVWHUR /·XOWLPR LQGLFH HFRQRPLFR DQDOL]]DWR q TXHOOR UHODWLYR DO IDWWXUDWR HVWHUR LO TXDOH VL ULIHULVFH DOOD PHUFH YHQGXWD D GL IXRUL GHL FRQILQL GL VWDWR 3XUWURSSR TXHVWD VHULH FRPLQFLDQHOSRLFKpSULPDGLWDOHGDWDQRQHUDFRQVLGHUDWDQHOO·LQGDJLQH Information on Models Series Span (n°of obs.) Model Span (n°of obs.) Method PRE-ADJUSTMENT Transformation Mean Correction Correction for Trading Day Effects Correction for Easter Effects Correction for Outliers Critical t-value Corr. for Missing Obs. Corr. for Other Regr. Effects Specif. Of the ARIMA model Non-seas. MA (lag 1) value Non-seas. MA (lag 1) t-value Seasonal MA (lag 4) value Seasonal MA (lag 4) t-value Method of Estimation DECOMPOSITION Arima decomposition Seasonality Information on Diagnostics SA quality index (stand. to 10) STATISTICS ON RESIDUALS Ljung-Box on residuals Box-Pierce on residuals Ljung-Box on squared residuals Box-Pierce on squared residuals DESCRIPTION OF RESIDUALS Normality Skewness Kurtosis OUTLIERS Percentage of outliers Q4.2003 – Q2.2011 (31) Q4.2003 – Q2.2011 (31) Tramo/Seats None None None None Autom.:AO,LS,TC 3.000 None None (0 1 1)(0 1 1) (fixed) 0.5223 2.48 [-2.021, 2.021] 5% -0.6607 -2.81 [-2.021, 2.021] 5% Exact Maximum Likelihood Exact Seasonal model used 2.355 [0, 10] ad-hoc 10.68 [0, 18.30] 5% 2.76 [0, 5.99] 5% 10.17 [0, 18.30] 5% 2.11 [0, 5.99] 5% 2.90 [0, 5.99] 5% -0.80 [-0.94, 0.94] 5% 3.35 [1.12, 4.88] 5% 0.00% [0%, 5.0%] ad-hoc 34 &RPHSHUOHVHULHSUHFHGHQWHPHQWHDQDOL]]DWHVLqFRVWUXLWRLOJUDILFRFRQLGDWLJUH]]L HGHVWDJLRQDOL]]DWL )DWWXUDWRHVWHUR,QGLFHJUH]]RHGHVWDJLRQDOL]]DWRVX9LFHQ]D 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