Results: souvenir_id_est.sas

The Arima Procedure

Identification 1

The ARIMA Procedure

Descriptive Statistics

Name of Variable = y
Mean of Working Series 9.219999
Standard Deviation 0.785391
Number of Observations 84

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 103.55 6 <.0001 0.602 0.443 0.485 0.408 0.351 0.284
12 189.73 12 <.0001 0.297 0.314 0.332 0.228 0.325 0.650
18 214.57 18 <.0001 0.325 0.176 0.231 0.168 0.124 0.076
24 236.69 24 <.0001 0.086 0.110 0.123 0.030 0.104 0.374

Series Correlation Panel

Trend and Correlation Analysis for y

Identification 2

Descriptive Statistics

Name of Variable = y
Period(s) of Differencing 1
Mean of Working Series 0.049892
Standard Deviation 0.623858
Number of Observations 83
Observation(s) eliminated by differencing 1

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 19.85 6 0.0029 -0.308 -0.287 0.199 -0.026 0.019 -0.099
12 98.27 12 <.0001 -0.009 0.009 0.190 -0.265 -0.306 0.770
18 113.75 18 <.0001 -0.185 -0.289 0.170 -0.011 0.009 -0.067
24 172.26 24 <.0001 -0.016 0.009 0.154 -0.199 -0.249 0.606

Series Correlation Panel

Trend and Correlation Analysis for y(1)

Identification 3

Descriptive Statistics

Name of Variable = y
Period(s) of Differencing 12
Mean of Working Series 0.288627
Standard Deviation 0.221759
Number of Observations 72
Observation(s) eliminated by differencing 12

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 44.53 6 <.0001 0.513 0.461 0.214 0.152 0.148 0.137
12 55.12 12 <.0001 0.128 0.194 0.198 0.117 -0.010 -0.134
18 56.54 18 <.0001 -0.073 -0.069 -0.022 -0.031 -0.015 -0.058
24 69.09 24 <.0001 -0.077 -0.065 -0.195 -0.093 -0.150 -0.194

Series Correlation Panel

Trend and Correlation Analysis for y(12)

Identification 4

Descriptive Statistics

Name of Variable = y
Period(s) of Differencing 1,12
Mean of Working Series -0.00207
Standard Deviation 0.219851
Number of Observations 71
Observation(s) eliminated by differencing 13

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 21.09 6 0.0018 -0.461 0.194 -0.169 -0.064 0.013 -0.004
12 26.20 12 0.0100 -0.074 0.071 0.094 0.023 0.005 -0.199
18 27.79 18 0.0653 0.077 -0.051 0.067 -0.028 0.054 -0.023
24 40.16 24 0.0206 -0.045 0.151 -0.241 0.176 -0.013 -0.071

Series Correlation Panel

Trend and Correlation Analysis for y(1 12)

The Arima Procedure

Identification 1

The ARIMA Procedure

Descriptive Statistics

Name of Variable = y
Period(s) of Differencing 12
Mean of Working Series 0.288627
Standard Deviation 0.221759
Number of Observations 72
Observation(s) eliminated by differencing 12

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 44.53 6 <.0001 0.513 0.461 0.214 0.152 0.148 0.137
12 55.12 12 <.0001 0.128 0.194 0.198 0.117 -0.010 -0.134
18 56.54 18 <.0001 -0.073 -0.069 -0.022 -0.031 -0.015 -0.058
24 69.09 24 <.0001 -0.077 -0.065 -0.195 -0.093 -0.150 -0.194

Series Correlation Panel

Trend and Correlation Analysis for y(12)

Estimation 1

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.29573 0.06065 4.88 <.0001 0
AR1,1 0.36049 0.11496 3.14 0.0017 1
AR1,2 0.29225 0.11450 2.55 0.0107 2

Fit Statistics

Constant Estimate 0.102695
Variance Estimate 0.034581
Std Error Estimate 0.185959
AIC -34.4995
SBC -27.6695
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU AR1,1 AR1,2
MU 1.000 0.013 -0.007
AR1,1 0.013 1.000 -0.520
AR1,2 -0.007 -0.520 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 2.78 4 0.5951 0.045 0.058 -0.127 -0.119 0.010 -0.006
12 12.94 10 0.2268 -0.040 0.124 0.184 0.106 -0.068 -0.226
18 13.57 16 0.6304 -0.037 -0.014 0.040 0.010 0.048 -0.033
24 18.78 22 0.6588 -0.004 0.052 -0.188 0.082 -0.002 -0.069

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.295728
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 - 0.36049 B**(1) - 0.29225 B**(2)

Estimation 2

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.28807 0.03996 7.21 <.0001 0
MA1,1 -0.33194 0.09955 -3.33 0.0009 1
MA1,2 -0.53264 0.10638 -5.01 <.0001 2

Fit Statistics

Constant Estimate 0.288067
Variance Estimate 0.03409
Std Error Estimate 0.184636
AIC -35.2912
SBC -28.4612
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 MA1,2
MU 1.000 -0.002 0.003
MA1,1 -0.002 1.000 0.236
MA1,2 0.003 0.236 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 3.32 4 0.5063 0.085 0.007 0.155 0.056 0.048 0.078
12 10.99 10 0.3587 0.002 0.080 0.168 0.129 -0.080 -0.177
18 12.41 16 0.7155 0.039 -0.009 -0.047 0.020 0.027 -0.099
24 20.77 22 0.5350 0.019 0.024 -0.236 0.038 -0.016 -0.143

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.288067
Period(s) of Differencing 12

Moving Average Factors

Moving Average Factors
Factor 1: 1 + 0.33194 B**(1) + 0.53264 B**(2)

Estimation 3

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.29635 0.06079 4.88 <.0001 0
MA1,1 0.35791 0.19491 1.84 0.0663 1
AR1,1 0.77422 0.13028 5.94 <.0001 1

Fit Statistics

Constant Estimate 0.066909
Variance Estimate 0.035716
Std Error Estimate 0.188985
AIC -32.2505
SBC -25.4205
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 AR1,1
MU 1.000 -0.017 -0.011
MA1,1 -0.017 1.000 0.818
AR1,1 -0.011 0.818 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 4.51 4 0.3416 -0.029 0.168 -0.142 -0.097 -0.016 -0.006
12 12.64 10 0.2448 -0.028 0.118 0.160 0.084 -0.041 -0.212
18 13.31 16 0.6501 -0.026 -0.041 0.043 0.000 0.050 -0.020
24 19.13 22 0.6375 -0.022 0.070 -0.189 0.088 -0.019 -0.076

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.296352
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 - 0.77422 B**(1)

Moving Average Factors

Moving Average Factors
Factor 1: 1 - 0.35791 B**(1)

Estimation 4

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.28447 0.03229 8.81 <.0001 0
MA1,1 -0.32112 0.09654 -3.33 0.0009 1
MA1,2 -0.56306 0.10460 -5.38 <.0001 2
AR1,1 -0.25578 0.12213 -2.09 0.0362 12

Fit Statistics

Constant Estimate 0.357226
Variance Estimate 0.032503
Std Error Estimate 0.180285
AIC -36.9013
SBC -27.7946
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 MA1,2 AR1,1
MU 1.000 0.004 0.008 0.010
MA1,1 0.004 1.000 0.252 -0.111
MA1,2 0.008 0.252 1.000 0.090
AR1,1 0.010 -0.111 0.090 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 5.54 3 0.1365 0.098 0.019 0.209 0.087 0.049 0.088
12 11.33 9 0.2538 0.040 0.089 0.157 0.169 -0.071 0.006
18 13.47 15 0.5662 0.060 -0.039 -0.035 0.004 0.053 -0.114
24 24.39 21 0.2744 -0.053 0.015 -0.225 0.003 -0.043 -0.215

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.284465
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 + 0.25578 B**(12)

Moving Average Factors

Moving Average Factors
Factor 1: 1 + 0.32112 B**(1) + 0.56306 B**(2)

Estimation 5

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.27419 0.02149 12.76 <.0001 0
MA1,1 -0.33681 0.09313 -3.62 0.0003 1
MA1,2 -0.57181 0.10020 -5.71 <.0001 2
MA2,1 0.54778 0.14127 3.88 0.0001 12

Fit Statistics

Constant Estimate 0.27419
Variance Estimate 0.029372
Std Error Estimate 0.171383
AIC -40.7347
SBC -31.628
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 MA1,2 MA2,1
MU 1.000 0.010 0.014 -0.173
MA1,1 0.010 1.000 0.293 0.028
MA1,2 0.014 0.293 1.000 -0.024
MA2,1 -0.173 0.028 -0.024 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 4.57 3 0.2059 0.078 0.020 0.207 0.072 0.050 0.047
12 11.34 9 0.2529 0.035 0.077 0.130 0.152 -0.067 0.163
18 14.11 15 0.5170 0.061 -0.041 -0.020 -0.022 0.061 -0.136
24 21.64 21 0.4207 -0.066 0.024 -0.214 -0.002 -0.081 -0.118

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.27419
Period(s) of Differencing 12

Moving Average Factors

Moving Average Factors
Factor 1: 1 + 0.33681 B**(1) + 0.57181 B**(2)
Factor 2: 1 - 0.54778 B**(12)

Estimation 6

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.27555 0.02520 10.93 <.0001 0
MA1,1 -0.41736 0.11871 -3.52 0.0004 1
MA1,2 -0.60113 0.11659 -5.16 <.0001 2
MA1,3 -0.12300 0.12199 -1.01 0.3133 3
MA2,1 0.50857 0.13829 3.68 0.0002 12

Fit Statistics

Constant Estimate 0.275553
Variance Estimate 0.029583
Std Error Estimate 0.171996
AIC -39.9033
SBC -28.52
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 MA1,2 MA1,3 MA2,1
MU 1.000 -0.016 -0.004 -0.030 -0.144
MA1,1 -0.016 1.000 0.468 0.625 0.093
MA1,2 -0.004 0.468 1.000 0.439 0.036
MA1,3 -0.030 0.625 0.439 1.000 0.095
MA2,1 -0.144 0.093 0.036 0.095 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 2.30 2 0.3171 0.002 -0.006 0.124 0.092 0.076 0.005
12 8.55 8 0.3816 0.002 0.098 0.112 0.134 -0.096 0.151
18 11.05 14 0.6822 0.049 -0.044 -0.016 -0.023 0.080 -0.119
24 17.58 20 0.6150 -0.072 0.049 -0.200 0.014 -0.075 -0.094

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.275553
Period(s) of Differencing 12

Moving Average Factors

Moving Average Factors
Factor 1: 1 + 0.41736 B**(1) + 0.60113 B**(2) + 0.123 B**(3)
Factor 2: 1 - 0.50857 B**(12)

Estimation 7

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.29648 0.05330 5.56 <.0001 0
AR1,1 0.34924 0.11140 3.13 0.0017 1
AR1,2 0.36017 0.11263 3.20 0.0014 2
AR2,1 -0.32761 0.11963 -2.74 0.0062 12

Fit Statistics

Constant Estimate 0.11438
Variance Estimate 0.031812
Std Error Estimate 0.178358
AIC -38.0893
SBC -28.9826
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU AR1,1 AR1,2 AR2,1
MU 1.000 0.026 0.027 -0.013
AR1,1 0.026 1.000 -0.535 0.033
AR1,2 0.027 -0.535 1.000 -0.197
AR2,1 -0.013 0.033 -0.197 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 2.36 3 0.5007 0.036 0.042 -0.083 -0.138 -0.002 -0.035
12 8.27 9 0.5071 -0.044 0.115 0.129 0.176 -0.080 0.019
18 10.00 15 0.8199 -0.025 -0.059 0.019 -0.030 0.105 -0.042
24 16.64 21 0.7328 -0.073 0.063 -0.164 0.061 -0.003 -0.150

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.296479
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 - 0.34924 B**(1) - 0.36017 B**(2)
Factor 2: 1 + 0.32761 B**(12)

Estimation 8

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.28562 0.03657 7.81 <.0001 0
MA1,1 0.52048 0.13629 3.82 0.0001 12
AR1,1 0.34695 0.11029 3.15 0.0017 1
AR1,2 0.35167 0.11058 3.18 0.0015 2

Fit Statistics

Constant Estimate 0.086079
Variance Estimate 0.029522
Std Error Estimate 0.17182
AIC -41.0894
SBC -31.9828
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 AR1,1 AR1,2
MU 1.000 -0.063 0.043 0.046
MA1,1 -0.063 1.000 -0.062 0.167
AR1,1 0.043 -0.062 1.000 -0.524
AR1,2 0.046 0.167 -0.524 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 2.74 3 0.4341 0.038 0.049 -0.084 -0.134 0.002 -0.078
12 9.08 9 0.4300 -0.054 0.092 0.105 0.166 -0.076 0.133
18 11.10 15 0.7454 -0.020 -0.049 0.002 -0.066 0.091 -0.074
24 15.48 21 0.7983 -0.060 0.069 -0.163 0.070 -0.031 -0.031

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.285617
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 - 0.34695 B**(1) - 0.35167 B**(2)

Moving Average Factors

Moving Average Factors
Factor 1: 1 - 0.52048 B**(12)

Estimation 9

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.28585 0.04178 6.84 <.0001 0
AR1,1 0.34024 0.11096 3.07 0.0022 1
AR1,2 0.31666 0.11044 2.87 0.0041 2
AR1,3 -0.18476 0.09540 -1.94 0.0528 12

Fit Statistics

Constant Estimate 0.150883
Variance Estimate 0.033237
Std Error Estimate 0.182311
AIC -35.7274
SBC -26.6207
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU AR1,1 AR1,2 AR1,3
MU 1.000 0.008 0.009 0.015
AR1,1 0.008 1.000 -0.529 0.141
AR1,2 0.009 -0.529 1.000 -0.080
AR1,3 0.015 0.141 -0.080 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 2.07 3 0.5580 0.060 0.056 -0.094 -0.103 0.023 -0.003
12 8.04 9 0.5303 -0.038 0.120 0.147 0.119 -0.090 -0.100
18 9.19 15 0.8675 0.008 0.033 0.064 0.002 0.055 -0.062
24 14.93 21 0.8262 -0.056 0.029 -0.187 0.069 0.010 -0.103

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.285845
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 - 0.34024 B**(1) - 0.31666 B**(2) + 0.18476 B**(12)

Estimation 10

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.29261 0.05009 5.84 <.0001 0
AR1,1 0.36513 0.11155 3.27 0.0011 1
AR1,2 0.32434 0.10758 3.01 0.0026 2
AR1,3 -0.26874 0.11214 -2.40 0.0166 12
AR1,4 0.15400 0.11597 1.33 0.1842 13

Fit Statistics

Constant Estimate 0.124436
Variance Estimate 0.032866
Std Error Estimate 0.18129
AIC -35.1832
SBC -23.7998
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU AR1,1 AR1,2 AR1,3 AR1,4
MU 1.000 0.029 0.006 0.004 0.032
AR1,1 0.029 1.000 -0.496 -0.073 0.246
AR1,2 0.006 -0.496 1.000 -0.029 -0.063
AR1,3 0.004 -0.073 -0.029 1.000 -0.529
AR1,4 0.032 0.246 -0.063 -0.529 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 2.44 2 0.2953 0.029 0.053 -0.098 -0.134 0.007 -0.010
12 8.25 8 0.4095 -0.059 0.131 0.137 0.147 -0.079 -0.036
18 9.64 14 0.7878 -0.066 -0.000 0.032 -0.007 0.086 -0.043
24 15.11 20 0.7698 -0.058 0.051 -0.162 0.059 0.002 -0.125

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.292608
Period(s) of Differencing 12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 - 0.36513 B**(1) - 0.32434 B**(2) + 0.26874 B**(12) - 0.154 B**(13)

Estimation 11

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.28471 0.03314 8.59 <.0001 0
MA1,1 -0.35951 0.10501 -3.42 0.0006 1
MA1,2 -0.58973 0.11222 -5.26 <.0001 2
MA1,3 0.33844 0.13195 2.56 0.0103 12

Fit Statistics

Constant Estimate 0.284714
Variance Estimate 0.030663
Std Error Estimate 0.175109
AIC -38.9406
SBC -29.834
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 MA1,2 MA1,3
MU 1.000 0.002 0.021 -0.033
MA1,1 0.002 1.000 0.379 0.094
MA1,2 0.021 0.379 1.000 -0.329
MA1,3 -0.033 0.094 -0.329 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 4.15 3 0.2455 0.073 0.056 0.181 0.024 0.069 0.084
12 11.09 9 0.2697 0.050 0.054 0.137 0.217 -0.097 0.024
18 13.17 15 0.5892 -0.010 -0.112 0.040 -0.022 0.038 -0.077
24 22.08 21 0.3951 -0.056 0.021 -0.200 0.039 -0.084 -0.176

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.284714
Period(s) of Differencing 12

Moving Average Factors

Moving Average Factors
Factor 1: 1 + 0.35951 B**(1) + 0.58973 B**(2) - 0.33844 B**(12)

Estimation 12

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU 0.28615 0.03436 8.33 <.0001 0
MA1,1 -0.35642 0.10812 -3.30 0.0010 1
MA1,2 -0.59039 0.12188 -4.84 <.0001 2
MA1,3 0.32764 0.13651 2.40 0.0164 12
MA1,4 -0.05761 0.12206 -0.47 0.6370 13

Fit Statistics

Constant Estimate 0.28615
Variance Estimate 0.030977
Std Error Estimate 0.176004
AIC -37.0801
SBC -25.6967
Number of Residuals 72

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 MA1,2 MA1,3 MA1,4
MU 1.000 0.002 0.008 -0.034 -0.035
MA1,1 0.002 1.000 0.345 0.004 -0.061
MA1,2 0.008 0.345 1.000 -0.312 0.297
MA1,3 -0.034 0.004 -0.312 1.000 0.098
MA1,4 -0.035 -0.061 0.297 0.098 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 4.06 2 0.1314 0.086 0.057 0.168 0.022 0.078 0.083
12 10.96 8 0.2038 0.044 0.059 0.142 0.214 -0.095 0.010
18 12.89 14 0.5352 -0.042 -0.093 0.050 -0.036 0.042 -0.066
24 21.36 20 0.3762 -0.056 0.017 -0.194 0.037 -0.087 -0.170

Residual Correlation Panel

Residual Correlation Diagnostics for y(12)

Residual Normality Panel

Residual Normality Diagnostics for y(12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean 0.28615
Period(s) of Differencing 12

Moving Average Factors

Moving Average Factors
Factor 1: 1 + 0.35642 B**(1) + 0.59039 B**(2) - 0.32764 B**(12) + 0.05761 B**(13)

The Arima Procedure

Identification 1

The ARIMA Procedure

Descriptive Statistics

Name of Variable = y
Period(s) of Differencing 1,12
Mean of Working Series -0.00207
Standard Deviation 0.219851
Number of Observations 71
Observation(s) eliminated by differencing 13

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 21.09 6 0.0018 -0.461 0.194 -0.169 -0.064 0.013 -0.004
12 26.20 12 0.0100 -0.074 0.071 0.094 0.023 0.005 -0.199
18 27.79 18 0.0653 0.077 -0.051 0.067 -0.028 0.054 -0.023
24 40.16 24 0.0206 -0.045 0.151 -0.241 0.176 -0.013 -0.071

Series Correlation Panel

Trend and Correlation Analysis for y(1 12)

Estimation 1

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU -0.0037704 0.01590 -0.24 0.8125 0
AR1,1 -0.47346 0.10543 -4.49 <.0001 1

Fit Statistics

Constant Estimate -0.00556
Variance Estimate 0.03872
Std Error Estimate 0.196774
AIC -27.1351
SBC -22.6098
Number of Residuals 71

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU AR1,1
MU 1.000 0.000
AR1,1 0.000 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 6.01 5 0.3052 -0.005 -0.069 -0.184 -0.194 -0.021 -0.043
12 18.43 11 0.0722 -0.071 0.128 0.197 0.094 -0.103 -0.256
18 19.32 17 0.3104 -0.030 0.010 0.060 0.026 0.055 -0.036
24 24.90 23 0.3554 0.005 0.063 -0.175 0.125 0.042 -0.038

Residual Correlation Panel

Residual Correlation Diagnostics for y(1 12)

Residual Normality Panel

Residual Normality Diagnostics for y(1 12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean -0.00377
Period(s) of Differencing 1,12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 + 0.47346 B**(1)

Estimation 2

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MU -0.0018114 0.0084264 -0.21 0.8298 0
MA1,1 0.51002 0.13626 3.74 0.0002 12
AR1,1 -0.50216 0.10109 -4.97 <.0001 1

Fit Statistics

Constant Estimate -0.00272
Variance Estimate 0.032463
Std Error Estimate 0.180176
AIC -35.034
SBC -28.246
Number of Residuals 71

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MU MA1,1 AR1,1
MU 1.000 -0.028 0.010
MA1,1 -0.028 1.000 -0.117
AR1,1 0.010 -0.117 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 4.99 4 0.2879 -0.013 -0.059 -0.109 -0.183 -0.031 -0.120
12 11.14 10 0.3468 -0.090 0.091 0.118 0.128 -0.116 0.111
18 13.39 16 0.6442 -0.015 -0.066 0.017 -0.051 0.107 -0.070
24 17.72 22 0.7227 -0.052 0.100 -0.139 0.100 0.006 0.003

Residual Correlation Panel

Residual Correlation Diagnostics for y(1 12)

Residual Normality Panel

Residual Normality Diagnostics for y(1 12)

Model Filters

Model for variable y

Model for variable y
Estimated Mean -0.00181
Period(s) of Differencing 1,12

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 + 0.50216 B**(1)

Moving Average Factors

Moving Average Factors
Factor 1: 1 - 0.51002 B**(12)

Estimation 3

Maximum Likelihood Estimation

Maximum Likelihood Estimation
Parameter Estimate Standard
Error		 t Value Approx
Pr > |t|		 Lag
MA1,1 0.51072 0.13525 3.78 0.0002 12
AR1,1 -0.50170 0.10036 -5.00 <.0001 1

Fit Statistics

Variance Estimate 0.032009
Std Error Estimate 0.17891
AIC -36.9884
SBC -32.463
Number of Residuals 71

Correlations of Parameter Estimates

Correlations of Parameter Estimates
Parameter MA1,1 AR1,1
MA1,1 1.000 -0.116
AR1,1 -0.116 1.000

Autocorrelation Check of Residuals

Autocorrelation Check of Residuals
To Lag Chi-Square DF Pr > ChiSq Autocorrelations
6 4.99 4 0.2881 -0.013 -0.058 -0.109 -0.184 -0.031 -0.119
12 11.14 10 0.3463 -0.089 0.090 0.118 0.129 -0.116 0.112
18 13.40 16 0.6434 -0.015 -0.066 0.016 -0.052 0.107 -0.069
24 17.72 22 0.7225 -0.050 0.100 -0.138 0.100 0.006 0.004

Residual Correlation Panel

Residual Correlation Diagnostics for y(1 12)

Residual Normality Panel

Residual Normality Diagnostics for y(1 12)

Model Filters

Model for variable y

Model for variable y
Period(s) of Differencing 1,12

No mean term in this model.

Autoregressive Factors

Autoregressive Factors
Factor 1: 1 + 0.5017 B**(1)

Moving Average Factors

Moving Average Factors
Factor 1: 1 - 0.51072 B**(12)