Results: monthly_temp_trend_less2.sas

The Print Procedure

Data Set WORK.BBB


Obs	time	temp	x1	x2	xsin1	xcos1	xsin2	xcos2	xsin3	xcos3	xsin4	xcos4	xsin5	xcos5	xcos6
1	1	2.7	0.08333	0.00694	0.50000	0.86603	0.86603	0.5	1	0	0.86603	-0.5	0.50000	-0.86603	-1
2	2	5.9	0.16667	0.02778	0.86603	0.50000	0.86603	-0.5	0	-1	-0.86603	-0.5	-0.86603	0.50000	1
3	3	5.1	0.25000	0.06250	1.00000	0.00000	0.00000	-1.0	-1	-0	-0.00000	1.0	1.00000	0.00000	-1
4	4	9.9	0.33333	0.11111	0.86603	-0.50000	-0.86603	-0.5	-0	1	0.86603	-0.5	-0.86603	-0.50000	1
5	5	10.7	0.41667	0.17361	0.50000	-0.86603	-0.86603	0.5	1	0	-0.86603	-0.5	0.50000	0.86603	-1
6	6	13.1	0.50000	0.25000	0.00000	-1.00000	-0.00000	1.0	0	-1	-0.00000	1.0	0.00000	-1.00000	1
7	7	16.3	0.58333	0.34028	-0.50000	-0.86603	0.86603	0.5	-1	-0	0.86603	-0.5	-0.50000	0.86603	-1
8	8	14.7	0.66667	0.44444	-0.86603	-0.50000	0.86603	-0.5	-0	1	-0.86603	-0.5	0.86603	-0.50000	1
9	9	14.0	0.75000	0.56250	-1.00000	-0.00000	0.00000	-1.0	1	0	-0.00000	1.0	-1.00000	0.00000	-1
10	10	9.8	0.83333	0.69444	-0.86603	0.50000	-0.86603	-0.5	0	-1	0.86603	-0.5	0.86603	0.50000	1
11	11	8.1	0.91667	0.84028	-0.50000	0.86603	-0.86603	0.5	-1	0	-0.86603	-0.5	-0.50000	-0.86603	-1
12	12	3.1	1.00000	1.00000	-0.00000	1.00000	-0.00000	1.0	-0	1	-0.00000	1.0	-0.00000	1.00000	1

The Print Procedure

Data Set WORK.BBB


Obs	time	temp	x1	x2	xsin1	xcos1	xsin2	xcos2	xsin3	xcos3	xsin4	xcos4	xsin5	xcos5	xcos6
289	289	3.7	24.0833	580.007	0.50000	0.86603	0.86603	0.5	1	0	0.86603	-0.5	0.50000	-0.86603	-1
290	290	2.9	24.1667	584.028	0.86603	0.50000	0.86603	-0.5	0	-1	-0.86603	-0.5	-0.86603	0.50000	1
291	291	3.7	24.2500	588.063	1.00000	0.00000	0.00000	-1.0	-1	0	-0.00000	1.0	1.00000	0.00000	-1
292	292	6.7	24.3333	592.111	0.86603	-0.50000	-0.86603	-0.5	0	1	0.86603	-0.5	-0.86603	-0.50000	1
293	293	13.0	24.4167	596.174	0.50000	-0.86603	-0.86603	0.5	1	0	-0.86603	-0.5	0.50000	0.86603	-1
294	294	16.4	24.5000	600.250	-0.00000	-1.00000	0.00000	1.0	0	-1	0.00000	1.0	0.00000	-1.00000	1
295	295	15.2	24.5833	604.340	-0.50000	-0.86603	0.86603	0.5	-1	0	0.86603	-0.5	-0.50000	0.86603	-1
296	296	16.0	24.6667	608.444	-0.86603	-0.50000	0.86603	-0.5	-0	1	-0.86603	-0.5	0.86603	-0.50000	1
297	297	14.4	24.7500	612.563	-1.00000	0.00000	-0.00000	-1.0	1	0	0.00000	1.0	-1.00000	0.00000	-1
298	298	10.7	24.8333	616.694	-0.86603	0.50000	-0.86603	-0.5	0	-1	0.86603	-0.5	0.86603	0.50000	1
299	299	7.8	24.9167	620.840	-0.50000	0.86603	-0.86603	0.5	-1	-0	-0.86603	-0.5	-0.50000	-0.86603	-1
300	300	4.3	25.0000	625.000	0.00000	1.00000	0.00000	1.0	-0	1	0.00000	1.0	-0.00000	1.00000	1
301	301	.	25.0833	629.174	0.50000	0.86603	0.86603	0.5	1	0	0.86603	-0.5	0.50000	-0.86603	-1
302	302	.	25.1667	633.361	0.86603	0.50000	0.86603	-0.5	-0	-1	-0.86603	-0.5	-0.86603	0.50000	1
303	303	.	25.2500	637.563	1.00000	0.00000	0.00000	-1.0	-1	0	-0.00000	1.0	1.00000	-0.00000	-1
304	304	.	25.3333	641.778	0.86603	-0.50000	-0.86603	-0.5	-0	1	0.86603	-0.5	-0.86603	-0.50000	1
305	305	.	25.4167	646.007	0.50000	-0.86603	-0.86603	0.5	1	0	-0.86603	-0.5	0.50000	0.86603	-1
306	306	.	25.5000	650.250	0.00000	-1.00000	-0.00000	1.0	0	-1	-0.00000	1.0	0.00000	-1.00000	1
307	307	.	25.5833	654.507	-0.50000	-0.86603	0.86603	0.5	-1	-0	0.86603	-0.5	-0.50000	0.86603	-1
308	308	.	25.6667	658.778	-0.86603	-0.50000	0.86603	-0.5	-0	1	-0.86603	-0.5	0.86603	-0.50000	1
309	309	.	25.7500	663.063	-1.00000	-0.00000	0.00000	-1.0	1	0	-0.00000	1.0	-1.00000	0.00000	-1
310	310	.	25.8333	667.361	-0.86603	0.50000	-0.86603	-0.5	0	-1	0.86603	-0.5	0.86603	0.50000	1
311	311	.	25.9167	671.674	-0.50000	0.86603	-0.86603	0.5	-1	-0	-0.86603	-0.5	-0.50000	-0.86603	-1
312	312	.	26.0000	676.000	-0.00000	1.00000	-0.00000	1.0	-0	1	-0.00000	1.0	-0.00000	1.00000	1
313	313	.	26.0833	680.340	0.50000	0.86603	0.86603	0.5	1	-0	0.86603	-0.5	0.50000	-0.86603	-1
314	314	.	26.1667	684.694	0.86603	0.50000	0.86603	-0.5	-0	-1	-0.86603	-0.5	-0.86603	0.50000	1
315	315	.	26.2500	689.063	1.00000	-0.00000	-0.00000	-1.0	-1	-0	0.00000	1.0	1.00000	0.00000	-1
316	316	.	26.3333	693.444	0.86603	-0.50000	-0.86603	-0.5	-0	1	0.86603	-0.5	-0.86603	-0.50000	1
317	317	.	26.4167	697.840	0.50000	-0.86603	-0.86603	0.5	1	0	-0.86603	-0.5	0.50000	0.86603	-1
318	318	.	26.5000	702.250	0.00000	-1.00000	-0.00000	1.0	0	-1	-0.00000	1.0	0.00000	-1.00000	1
319	319	.	26.5833	706.674	-0.50000	-0.86603	0.86603	0.5	-1	-0	0.86603	-0.5	-0.50000	0.86603	-1
320	320	.	26.6667	711.111	-0.86603	-0.50000	0.86603	-0.5	-0	1	-0.86603	-0.5	0.86603	-0.50000	1
321	321	.	26.7500	715.563	-1.00000	-0.00000	0.00000	-1.0	1	0	-0.00000	1.0	-1.00000	0.00000	-1
322	322	.	26.8333	720.028	-0.86603	0.50000	-0.86603	-0.5	0	-1	0.86603	-0.5	0.86603	0.50000	1
323	323	.	26.9167	724.507	-0.50000	0.86603	-0.86603	0.5	-1	-0	-0.86603	-0.5	-0.50000	-0.86603	-1
324	324	.	27.0000	729.000	-0.00000	1.00000	-0.00000	1.0	0	1	-0.00000	1.0	-0.00000	1.00000	1

The ARIMA Procedure

The Arima Procedure

Estimation 1

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.78647	0.23837	41.06	<.0001	0	temp	0
NUM1	-0.03917	0.04387	-0.89	0.3720	0	x1	0
NUM2	0.0008569	0.0016939	0.51	0.6129	0	x2	0
NUM3	-4.06074	0.11164	-36.37	<.0001	0	xsin1	0
NUM4	-5.00481	0.11160	-44.85	<.0001	0	xcos1	0
NUM5	0.22838	0.11160	2.05	0.0407	0	xsin2	0
NUM6	-0.13188	0.11160	-1.18	0.2373	0	xcos2	0
NUM7	0.08652	0.11160	0.78	0.4382	0	xsin3	0
NUM8	-0.06520	0.11160	-0.58	0.5590	0	xcos3	0
NUM9	0.15157	0.11159	1.36	0.1744	0	xsin4	0
NUM10	0.09080	0.11160	0.81	0.4158	0	xcos4	0
NUM11	0.08283	0.11159	0.74	0.4579	0	xsin5	0
NUM12	-0.02566	0.11160	-0.23	0.8181	0	xcos5	0
NUM13	0.0020697	0.07891	0.03	0.9791	0	xcos6	0

Fit Statistics


Constant Estimate	9.786474
Variance Estimate	1.867893
Std Error Estimate	1.366709
AIC	1052.469
SBC	1104.322
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	x1 NUM1	x2 NUM2	xsin1 NUM3	xcos1 NUM4	xsin2 NUM5	xcos2 NUM6	xsin3 NUM7	xcos3 NUM8	xsin4 NUM9	xcos4 NUM10	xsin5 NUM11	xcos5 NUM12	xcos6 NUM13
temp MU	1.000	-0.868	0.748	-0.018	0.004	-0.008	0.004	-0.005	0.005	-0.003	0.005	-0.001	0.005	0.003
x1 NUM1	-0.868	1.000	-0.968	0.008	-0.001	0.004	-0.002	0.002	-0.002	0.001	-0.002	0.001	-0.002	-0.001
x2 NUM2	0.748	-0.968	1.000	-0.000	-0.001	-0.000	-0.000	-0.000	-0.000	-0.000	-0.000	-0.000	-0.000	0.000
xsin1 NUM3	-0.018	0.008	-0.000	1.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	-0.000
xcos1 NUM4	0.004	-0.001	-0.001	-0.000	1.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	0.000
xsin2 NUM5	-0.008	0.004	-0.000	0.000	-0.000	1.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	-0.000
xcos2 NUM6	0.004	-0.002	-0.000	-0.000	0.000	-0.000	1.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	0.000
xsin3 NUM7	-0.005	0.002	-0.000	0.000	-0.000	0.000	-0.000	1.000	-0.000	0.000	-0.000	0.000	-0.000	-0.000
xcos3 NUM8	0.005	-0.002	-0.000	-0.000	0.000	-0.000	0.000	-0.000	1.000	-0.000	0.000	-0.000	0.000	0.000
xsin4 NUM9	-0.003	0.001	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	1.000	-0.000	0.000	-0.000	-0.000
xcos4 NUM10	0.005	-0.002	-0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	1.000	-0.000	0.000	0.000
xsin5 NUM11	-0.001	0.001	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	1.000	-0.000	-0.000
xcos5 NUM12	0.005	-0.002	-0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	1.000	0.000
xcos6 NUM13	0.003	-0.001	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	34.55	6	<.0001	0.294	0.130	0.083	0.058	-0.023	-0.001
12	40.80	12	<.0001	0.043	0.059	0.067	0.050	-0.023	-0.085
18	48.81	18	0.0001	-0.003	-0.129	-0.077	-0.028	0.015	0.041
24	58.06	24	0.0001	0.107	0.059	0.055	-0.082	-0.057	-0.023
30	59.73	30	0.0010	0.034	-0.021	0.014	0.044	0.033	-0.014
36	78.25	36	<.0001	0.005	-0.098	-0.125	-0.009	-0.092	-0.143
42	91.66	42	<.0001	-0.135	-0.059	-0.027	-0.022	-0.036	-0.120
48	93.95	48	<.0001	-0.032	0.052	-0.015	-0.036	0.024	-0.024

Residual Correlation Panel

Residual Correlation Diagnostics for temp

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.786474

Input Number 1


Input Number 1
Input Variable	x1
Overall Regression Factor	-0.03917

Input Number 2


Input Number 2
Input Variable	x2
Overall Regression Factor	0.000857

Input Number 3


Input Number 3
Input Variable	xsin1
Overall Regression Factor	-4.06074

Input Number 4


Input Number 4
Input Variable	xcos1
Overall Regression Factor	-5.00481

Input Number 5


Input Number 5
Input Variable	xsin2
Overall Regression Factor	0.228379

Input Number 6


Input Number 6
Input Variable	xcos2
Overall Regression Factor	-0.13188

Input Number 7


Input Number 7
Input Variable	xsin3
Overall Regression Factor	0.086521

Input Number 8


Input Number 8
Input Variable	xcos3
Overall Regression Factor	-0.0652

Input Number 9


Input Number 9
Input Variable	xsin4
Overall Regression Factor	0.151567

Input Number 10


Input Number 10
Input Variable	xcos4
Overall Regression Factor	0.090804

Input Number 11


Input Number 11
Input Variable	xsin5
Overall Regression Factor	0.082827

Input Number 12


Input Number 12
Input Variable	xcos5
Overall Regression Factor	-0.02566

Input Number 13


Input Number 13
Input Variable	xcos6
Overall Regression Factor	0.00207

Estimation 2

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.77313	0.32073	30.47	<.0001	0	temp	0
AR1,1	0.29334	0.05660	5.18	<.0001	1	temp	0
NUM1	-0.03712	0.05905	-0.63	0.5296	0	x1	0
NUM2	0.0007915	0.0022792	0.35	0.7284	0	x2	0
NUM3	-4.05990	0.14061	-28.87	<.0001	0	xsin1	0
NUM4	-5.00734	0.14025	-35.70	<.0001	0	xcos1	0
NUM5	0.22934	0.12004	1.91	0.0561	0	xsin2	0
NUM6	-0.13412	0.11990	-1.12	0.2633	0	xcos2	0
NUM7	0.08731	0.10254	0.85	0.3945	0	xsin3	0
NUM8	-0.06722	0.10254	-0.66	0.5121	0	xcos3	0
NUM9	0.15210	0.09098	1.67	0.0945	0	xsin4	0
NUM10	0.08890	0.09105	0.98	0.3289	0	xcos4	0
NUM11	0.08309	0.08462	0.98	0.3261	0	xsin5	0
NUM12	-0.02750	0.08473	-0.32	0.7455	0	xcos5	0
NUM13	0.0011604	0.05845	0.02	0.9842	0	xcos6	0

Fit Statistics


Constant Estimate	6.906252
Variance Estimate	1.712458
Std Error Estimate	1.308609
AIC	1027.444
SBC	1083.001
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp AR1,1	x1 NUM1	x2 NUM2	xsin1 NUM3	xcos1 NUM4	xsin2 NUM5	xcos2 NUM6	xsin3 NUM7	xcos3 NUM8	xsin4 NUM9	xcos4 NUM10	xsin5 NUM11	xcos5 NUM12	xcos6 NUM13
temp MU	1.000	0.000	-0.866	0.746	-0.019	-0.003	-0.011	-0.000	-0.007	0.002	-0.005	0.003	-0.002	0.004	0.003
temp AR1,1	0.000	1.000	-0.001	0.001	0.000	0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	-0.000
x1 NUM1	-0.866	-0.001	1.000	-0.968	0.010	0.007	0.006	0.003	0.005	0.001	0.003	-0.001	0.002	-0.002	-0.001
x2 NUM2	0.746	0.001	-0.968	1.000	-0.002	-0.009	-0.003	-0.005	-0.003	-0.003	-0.002	-0.001	-0.001	-0.000	-0.000
xsin1 NUM3	-0.019	0.000	0.010	-0.002	1.000	-0.001	0.001	-0.001	0.001	-0.001	0.000	-0.002	0.000	-0.002	-0.001
xcos1 NUM4	-0.003	0.000	0.007	-0.009	-0.001	1.000	-0.002	-0.003	-0.002	-0.001	-0.001	-0.000	-0.001	0.000	0.000
xsin2 NUM5	-0.011	0.000	0.006	-0.003	0.001	-0.002	1.000	-0.002	0.001	-0.002	0.000	-0.002	0.000	-0.002	-0.001
xcos2 NUM6	-0.000	-0.000	0.003	-0.005	-0.001	-0.003	-0.002	1.000	-0.002	-0.000	-0.001	0.000	-0.001	0.001	0.001
xsin3 NUM7	-0.007	0.000	0.005	-0.003	0.001	-0.002	0.001	-0.002	1.000	-0.002	0.000	-0.002	0.000	-0.002	-0.001
xcos3 NUM8	0.002	-0.000	0.001	-0.003	-0.001	-0.001	-0.002	-0.000	-0.002	1.000	-0.001	0.001	-0.001	0.002	0.001
xsin4 NUM9	-0.005	0.000	0.003	-0.002	0.000	-0.001	0.000	-0.001	0.000	-0.001	1.000	-0.001	0.000	-0.001	-0.001
xcos4 NUM10	0.003	-0.000	-0.001	-0.001	-0.002	-0.000	-0.002	0.000	-0.002	0.001	-0.001	1.000	-0.001	0.002	0.002
xsin5 NUM11	-0.002	0.000	0.002	-0.001	0.000	-0.001	0.000	-0.001	0.000	-0.001	0.000	-0.001	1.000	-0.001	-0.001
xcos5 NUM12	0.004	-0.000	-0.002	-0.000	-0.002	0.000	-0.002	0.001	-0.002	0.002	-0.001	0.002	-0.001	1.000	0.002
xcos6 NUM13	0.003	-0.000	-0.001	-0.000	-0.001	0.000	-0.001	0.001	-0.001	0.001	-0.001	0.002	-0.001	0.002	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	2.25	5	0.8130	-0.014	0.034	0.038	0.050	-0.046	-0.008
12	7.00	11	0.7992	0.033	0.035	0.044	0.045	-0.016	-0.093
18	14.14	17	0.6568	0.065	-0.128	-0.040	-0.013	0.013	0.010
24	22.47	23	0.4923	0.095	0.019	0.072	-0.097	-0.034	-0.020
30	25.05	29	0.6759	0.055	-0.040	0.009	0.038	0.029	-0.029
36	37.82	35	0.3416	0.042	-0.078	-0.114	0.059	-0.061	-0.097
42	46.15	41	0.2679	-0.095	-0.019	-0.006	-0.006	0.002	-0.120
48	50.58	47	0.3341	-0.017	0.077	-0.023	-0.046	0.048	-0.035

Residual Correlation Panel

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.773133

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.29334 B**(1)

Input Number 1


Input Number 1
Input Variable	x1
Overall Regression Factor	-0.03712

Input Number 2


Input Number 2
Input Variable	x2
Overall Regression Factor	0.000792

Input Number 3


Input Number 3
Input Variable	xsin1
Overall Regression Factor	-4.0599

Input Number 4


Input Number 4
Input Variable	xcos1
Overall Regression Factor	-5.00734

Input Number 5


Input Number 5
Input Variable	xsin2
Overall Regression Factor	0.229339

Input Number 6


Input Number 6
Input Variable	xcos2
Overall Regression Factor	-0.13412

Input Number 7


Input Number 7
Input Variable	xsin3
Overall Regression Factor	0.087314

Input Number 8


Input Number 8
Input Variable	xcos3
Overall Regression Factor	-0.06722

Input Number 9


Input Number 9
Input Variable	xsin4
Overall Regression Factor	0.152104

Input Number 10


Input Number 10
Input Variable	xcos4
Overall Regression Factor	0.088905

Input Number 11


Input Number 11
Input Variable	xsin5
Overall Regression Factor	0.083095

Input Number 12


Input Number 12
Input Variable	xcos5
Overall Regression Factor	-0.0275

Input Number 13


Input Number 13
Input Variable	xcos6
Overall Regression Factor	0.00116

Estimation 3

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.47361	0.10618	89.22	<.0001	0	temp	0
AR1,1	0.29100	0.05581	5.21	<.0001	1	temp	0
NUM1	-4.05520	0.13992	-28.98	<.0001	0	xsin1	0
NUM2	-5.00804	0.13962	-35.87	<.0001	0	xcos1	0
NUM3	0.23096	0.11997	1.93	0.0542	0	xsin2	0

Fit Statistics


Constant Estimate	6.716803
Variance Estimate	1.705269
Std Error Estimate	1.30586
AIC	1016.526
SBC	1035.045
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp AR1,1	xsin1 NUM1	xcos1 NUM2	xsin2 NUM3
temp MU	1.000	-0.001	-0.001	-0.003	-0.001
temp AR1,1	-0.001	1.000	-0.001	-0.001	0.068
xsin1 NUM1	-0.001	-0.001	1.000	-0.001	0.000
xcos1 NUM2	-0.003	-0.001	-0.001	1.000	-0.002
xsin2 NUM3	-0.001	0.068	0.000	-0.002	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	2.25	5	0.8136	-0.012	0.027	0.054	0.044	-0.039	0.007
12	5.65	11	0.8957	0.034	0.036	0.059	0.038	-0.018	-0.056
18	12.23	17	0.7862	0.056	-0.124	-0.024	-0.011	0.023	0.030
24	21.56	23	0.5467	0.098	0.016	0.090	-0.098	-0.034	0.011
30	24.07	29	0.7255	0.054	-0.045	0.019	0.038	0.029	-0.010
36	34.08	35	0.5122	0.043	-0.079	-0.097	0.055	-0.061	-0.072
42	40.86	41	0.4769	-0.089	-0.026	0.001	-0.008	0.004	-0.104
48	44.38	47	0.5816	-0.014	0.070	-0.014	-0.051	0.041	-0.018

Residual Correlation Panel

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.473607

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.291 B**(1)

Input Number 1


Input Number 1
Input Variable	xsin1
Overall Regression Factor	-4.0552

Input Number 2


Input Number 2
Input Variable	xcos1
Overall Regression Factor	-5.00804

Input Number 3


Input Number 3
Input Variable	xsin2
Overall Regression Factor	0.230964

Estimation 4

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.47387	0.10710	88.46	<.0001	0	temp	0
AR1,1	0.29392	0.05553	5.29	<.0001	1	temp	0
NUM1	-4.05530	0.14097	-28.77	<.0001	0	xsin1	0
NUM2	-5.00756	0.14066	-35.60	<.0001	0	xcos1	0

Fit Statistics


Constant Estimate	6.689294
Variance Estimate	1.720925
Std Error Estimate	1.31184
AIC	1018.285
SBC	1033.1
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp AR1,1	xsin1 NUM1	xcos1 NUM2
temp MU	1.000	-0.001	-0.001	-0.003
temp AR1,1	-0.001	1.000	-0.001	-0.000
xsin1 NUM1	-0.001	-0.001	1.000	-0.001
xcos1 NUM2	-0.003	-0.000	-0.001	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	1.52	5	0.9110	-0.009	0.019	0.041	0.037	-0.033	0.020
12	3.81	11	0.9752	0.039	0.027	0.046	0.034	-0.009	-0.042
18	11.82	17	0.8110	0.060	-0.130	-0.038	-0.018	0.030	0.045
24	21.03	23	0.5793	0.104	0.009	0.075	-0.103	-0.025	0.024
30	23.82	29	0.7378	0.058	-0.051	0.005	0.032	0.036	0.004
36	33.97	35	0.5175	0.048	-0.086	-0.109	0.049	-0.052	-0.058
42	39.73	41	0.5272	-0.082	-0.032	-0.010	-0.013	0.011	-0.092
48	43.26	47	0.6284	-0.009	0.064	-0.024	-0.054	0.046	-0.009

Residual Correlation Panel

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.473868

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.29392 B**(1)

Input Number 1


Input Number 1
Input Variable	xsin1
Overall Regression Factor	-4.0553

Input Number 2


Input Number 2
Input Variable	xcos1
Overall Regression Factor	-5.00756

Estimation 5

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.47335	0.10056	94.20	<.0001	0	temp	0
MA1,1	0.05633	0.05915	0.95	0.3410	12	temp	0
AR1,1	0.29188	0.05590	5.22	<.0001	1	temp	0
NUM1	-4.05418	0.13249	-30.60	<.0001	0	xsin1	0
NUM2	-5.00823	0.13218	-37.89	<.0001	0	xcos1	0
NUM3	0.23175	0.11355	2.04	0.0413	0	xsin2	0

Fit Statistics


Constant Estimate	6.708298
Variance Estimate	1.705576
Std Error Estimate	1.305977
AIC	1017.6
SBC	1039.823
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp MA1,1	temp AR1,1	xsin1 NUM1	xcos1 NUM2	xsin2 NUM3
temp MU	1.000	-0.002	-0.001	-0.001	-0.003	-0.001
temp MA1,1	-0.002	1.000	-0.006	0.015	0.002	0.004
temp AR1,1	-0.001	-0.006	1.000	-0.001	-0.001	0.072
xsin1 NUM1	-0.001	0.015	-0.001	1.000	-0.001	0.000
xcos1 NUM2	-0.003	0.002	-0.001	-0.001	1.000	-0.002
xsin2 NUM3	-0.001	0.004	0.072	0.000	-0.002	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	2.23	4	0.6933	-0.011	0.021	0.057	0.046	-0.036	0.010
12	5.09	10	0.8851	0.038	0.039	0.068	0.035	-0.021	-0.001
18	11.77	16	0.7599	0.059	-0.125	-0.020	-0.006	0.023	0.031
24	21.16	22	0.5106	0.103	0.014	0.089	-0.094	-0.039	0.006
30	23.87	28	0.6883	0.051	-0.053	0.018	0.037	0.030	-0.012
36	33.31	34	0.5012	0.048	-0.075	-0.093	0.046	-0.061	-0.073
42	39.88	40	0.4755	-0.086	-0.027	0.001	-0.005	0.003	-0.103
48	43.25	46	0.5882	-0.015	0.066	-0.021	-0.049	0.039	-0.023

Residual Correlation Panel

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.473352

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.29188 B**(1)

Moving Average Factors


Moving Average Factors
Factor 1:	1 - 0.05633 B**(12)

Input Number 1


Input Number 1
Input Variable	xsin1
Overall Regression Factor	-4.05418

Input Number 2


Input Number 2
Input Variable	xcos1
Overall Regression Factor	-5.00823

Input Number 3


Input Number 3
Input Variable	xsin2
Overall Regression Factor	0.231749

Estimation 6

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.47334	0.10084	93.95	<.0001	0	temp	0
AR1,1	0.29195	0.05589	5.22	<.0001	1	temp	0
AR2,1	-0.05664	0.05904	-0.96	0.3374	12	temp	0
NUM1	-4.05459	0.13284	-30.52	<.0001	0	xsin1	0
NUM2	-5.00840	0.13254	-37.79	<.0001	0	xcos1	0
NUM3	0.23165	0.11385	2.03	0.0419	0	xsin2	0

Fit Statistics


Constant Estimate	7.087549
Variance Estimate	1.705506
Std Error Estimate	1.30595
AIC	1017.589
SBC	1039.811
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp AR1,1	temp AR2,1	xsin1 NUM1	xcos1 NUM2	xsin2 NUM3
temp MU	1.000	-0.001	0.003	-0.001	-0.003	-0.001
temp AR1,1	-0.001	1.000	-0.001	-0.001	-0.001	0.072
temp AR2,1	0.003	-0.001	1.000	-0.011	-0.002	-0.004
xsin1 NUM1	-0.001	-0.001	-0.011	1.000	-0.001	0.000
xcos1 NUM2	-0.003	-0.001	-0.002	-0.001	1.000	-0.002
xsin2 NUM3	-0.001	0.072	-0.004	0.000	-0.002	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	2.23	4	0.6934	-0.011	0.022	0.056	0.046	-0.036	0.010
12	5.11	10	0.8836	0.037	0.039	0.068	0.035	-0.021	0.000
18	11.81	16	0.7571	0.059	-0.125	-0.020	-0.006	0.022	0.032
24	21.20	22	0.5084	0.103	0.013	0.089	-0.094	-0.039	0.003
30	23.92	28	0.6858	0.051	-0.053	0.018	0.036	0.030	-0.012
36	33.36	34	0.4989	0.048	-0.075	-0.093	0.046	-0.061	-0.073
42	39.93	40	0.4733	-0.086	-0.026	0.001	-0.005	0.003	-0.104
48	43.29	46	0.5863	-0.015	0.066	-0.022	-0.048	0.040	-0.023

Residual Correlation Panel

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.473342

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.29195 B**(1)
Factor 2:	1 + 0.05664 B**(12)

Input Number 1


Input Number 1
Input Variable	xsin1
Overall Regression Factor	-4.05459

Input Number 2


Input Number 2
Input Variable	xcos1
Overall Regression Factor	-5.0084

Input Number 3


Input Number 3
Input Variable	xsin2
Overall Regression Factor	0.231647

Estimation 7

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.47351	0.09990	94.83	<.0001	0	temp	0
AR1,1	0.29020	0.05583	5.20	<.0001	1	temp	0
AR1,2	-0.04605	0.05646	-0.82	0.4148	12	temp	0
NUM1	-4.05431	0.13235	-30.63	<.0001	0	xsin1	0
NUM2	-5.00859	0.13207	-37.92	<.0001	0	xcos1	0
NUM3	0.23089	0.11455	2.02	0.0438	0	xsin2	0

Fit Statistics


Constant Estimate	7.160537
Variance Estimate	1.707004
Std Error Estimate	1.306524
AIC	1017.84
SBC	1040.063
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp AR1,1	temp AR1,2	xsin1 NUM1	xcos1 NUM2	xsin2 NUM3
temp MU	1.000	-0.001	0.002	-0.001	-0.003	-0.001
temp AR1,1	-0.001	1.000	0.017	0.000	-0.001	0.067
temp AR1,2	0.002	0.017	1.000	-0.015	-0.001	0.018
xsin1 NUM1	-0.001	0.000	-0.015	1.000	-0.001	0.000
xcos1 NUM2	-0.003	-0.001	-0.001	-0.001	1.000	-0.002
xsin2 NUM3	-0.001	0.067	0.018	0.000	-0.002	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	2.27	4	0.6854	-0.011	0.023	0.057	0.047	-0.035	0.011
12	5.09	10	0.8849	0.038	0.039	0.065	0.036	-0.019	-0.010
18	11.93	16	0.7490	0.071	-0.121	-0.019	-0.006	0.023	0.032
24	21.29	22	0.5029	0.101	0.014	0.090	-0.095	-0.039	0.003
30	23.83	28	0.6906	0.050	-0.051	0.017	0.036	0.028	-0.012
36	33.53	34	0.4905	0.048	-0.075	-0.094	0.049	-0.063	-0.074
42	40.16	40	0.4632	-0.086	-0.026	0.000	-0.006	0.004	-0.104
48	43.61	46	0.5728	-0.015	0.066	-0.021	-0.050	0.039	-0.025

Residual Correlation Panel

Residual Normality Panel

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.473507

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.2902 B(1) + 0.04605 B(12)

Input Number 1


Input Number 1
Input Variable	xsin1
Overall Regression Factor	-4.05431

Input Number 2


Input Number 2
Input Variable	xcos1
Overall Regression Factor	-5.00859

Input Number 3


Input Number 3
Input Variable	xsin2
Overall Regression Factor	0.230887

The ARIMA Procedure

The Arima Procedure

Estimation 1

Maximum Likelihood Estimation


Maximum Likelihood Estimation
Parameter	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Lag	Variable	Shift
MU	9.47361	0.10618	89.22	<.0001	0	temp	0
AR1,1	0.29100	0.05581	5.21	<.0001	1	temp	0
NUM1	-4.05520	0.13992	-28.98	<.0001	0	xsin1	0
NUM2	-5.00804	0.13962	-35.87	<.0001	0	xcos1	0
NUM3	0.23096	0.11997	1.93	0.0542	0	xsin2	0

Fit Statistics


Constant Estimate	6.716803
Variance Estimate	1.705269
Std Error Estimate	1.30586
AIC	1016.526
SBC	1035.045
Number of Residuals	300

Correlations of Parameter Estimates


Correlations of Parameter Estimates
Variable Parameter	temp MU	temp AR1,1	xsin1 NUM1	xcos1 NUM2	xsin2 NUM3
temp MU	1.000	-0.001	-0.001	-0.003	-0.001
temp AR1,1	-0.001	1.000	-0.001	-0.001	0.068
xsin1 NUM1	-0.001	-0.001	1.000	-0.001	0.000
xcos1 NUM2	-0.003	-0.001	-0.001	1.000	-0.002
xsin2 NUM3	-0.001	0.068	0.000	-0.002	1.000

Autocorrelation Check of Residuals


Autocorrelation Check of Residuals
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	2.25	5	0.8136	-0.012	0.027	0.054	0.044	-0.039	0.007
12	5.65	11	0.8957	0.034	0.036	0.059	0.038	-0.018	-0.056
18	12.23	17	0.7862	0.056	-0.124	-0.024	-0.011	0.023	0.030
24	21.56	23	0.5467	0.098	0.016	0.090	-0.098	-0.034	0.011
30	24.07	29	0.7255	0.054	-0.045	0.019	0.038	0.029	-0.010
36	34.08	35	0.5122	0.043	-0.079	-0.097	0.055	-0.061	-0.072
42	40.86	41	0.4769	-0.089	-0.026	0.001	-0.008	0.004	-0.104
48	44.38	47	0.5816	-0.014	0.070	-0.014	-0.051	0.041	-0.018

Residual Correlation Panel

Residual Normality Panel

Residual Plot

Model Filters

Model for variable temp


Model for variable temp
Estimated Intercept	9.473607

Autoregressive Factors


Autoregressive Factors
Factor 1:	1 - 0.291 B**(1)

Input Number 1


Input Number 1
Input Variable	xsin1
Overall Regression Factor	-4.0552

Input Number 2


Input Number 2
Input Variable	xcos1
Overall Regression Factor	-5.00804

Input Number 3


Input Number 3
Input Variable	xsin2
Overall Regression Factor	0.230964

Forecast 1

Forecasts for temp


Forecasts for variable temp
Obs	Forecast	Std Error	95% Confidence Limits
301	3.2608	1.3059	0.7013	5.8202
302	3.6437	1.3600	0.9781	6.3093
303	5.4143	1.3645	2.7399	8.0887
304	8.2645	1.3649	5.5894	10.9397
305	11.5827	1.3649	8.9075	14.2579
306	14.4815	1.3649	11.8063	17.1568
307	16.0383	1.3649	13.3631	18.7135
308	15.6895	1.3649	13.0143	18.3648
309	13.5288	1.3649	10.8536	16.2040
310	10.2815	1.3649	7.6063	12.9567
311	6.9641	1.3649	4.2889	9.6393
312	4.4656	1.3649	1.7904	7.1408
313	3.3089	1.3649	0.6337	5.9841
314	3.6577	1.3649	0.9825	6.3329
315	5.4184	1.3649	2.7432	8.0936
316	8.2657	1.3649	5.5905	10.9409
317	11.5831	1.3649	8.9079	14.2583
318	14.4816	1.3649	11.8064	17.1569
319	16.0383	1.3649	13.3631	18.7135
320	15.6896	1.3649	13.0143	18.3648
321	13.5288	1.3649	10.8536	16.2040
322	10.2815	1.3649	7.6063	12.9567
323	6.9641	1.3649	4.2889	9.6393
324	4.4656	1.3649	1.7904	7.1408
325	3.3089	1.3649	0.6337	5.9841
326	3.6577	1.3649	0.9825	6.3329
327	5.4184	1.3649	2.7432	8.0936
328	8.2657	1.3649	5.5905	10.9409
329	11.5831	1.3649	8.9079	14.2583
330	14.4816	1.3649	11.8064	17.1569
331	16.0383	1.3649	13.3631	18.7135
332	15.6896	1.3649	13.0143	18.3648
333	13.5288	1.3649	10.8536	16.2040
334	10.2815	1.3649	7.6063	12.9567
335	6.9641	1.3649	4.2889	9.6393
336	4.4656	1.3649	1.7904	7.1408
337	3.3089	1.3649	0.6337	5.9841
338	3.6577	1.3649	0.9825	6.3329
339	5.4184	1.3649	2.7432	8.0936
340	8.2657	1.3649	5.5905	10.9409
341	11.5831	1.3649	8.9079	14.2583
342	14.4816	1.3649	11.8064	17.1569
343	16.0383	1.3649	13.3631	18.7135
344	15.6896	1.3649	13.0143	18.3648
345	13.5288	1.3649	10.8536	16.2040
346	10.2815	1.3649	7.6063	12.9567
347	6.9641	1.3649	4.2889	9.6393
348	4.4656	1.3649	1.7904	7.1408