Time Series

QUESTION 5

The time series plot in Figure 1.1 shows the monthly hotel room occupancy in the USA from 1977 to 1990 (168 observations). SPSS was used for analysis.

(e) Discuss the adequacy of Model 1 fitted in Figure 1.2 suggesting what could be done to make this model adequate.

1200 1000 800 Ada -009 400 FOCT 1990 MAY 1990 DEC 1989 JUL 1989 FEB 1989 SEP 1988 APR 1988 NOV 1987 JUN 1987 JAN 1987 FAUG 1986 MAR 1986 FOCT 1985 MAY 1985 DEC 1984 JUL 1984 FEB 1984 SEP 1983 APR 1983 NOV 1982 JUN 1982 JAN 1982 AUG 1981 MAR 1981 FOCT 1980 MAY 1980 DEC 1979 JUL 1979 FEB 1979 SEP 1978 APR 1978 NOV 1977 JUN 1977 JAN 1977 Date Figure 1.1: Monthly hotel room occupancy in the USA from Jan 1977 to Dec 1990 Hotel Occupancy Model 1 Hotel Occupancy Time $1 $2 S3 S4 $5 S6 S7 $8 S9 $10 $11 Model Hotel Occupancy- Model 1 Natural Log No Transformation No Transformation No Transformation No Transformation. No Transformation. No Transformation No Transformation No Transformation No Transformation No Transformation No Transformation No Transformation Number of Predictors ARIMA Model Parameters Constant Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator 12 Model Statistics Model Fit statistics. Stationary R- squared 989 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Ljung-Box Q(18) DF Statistics 96.328 Estimate 6.288 18 003 -042 -112 -084 040 020 147 289 311 056 040 -112 Sig. .000 SE t 006 978.262 3.379E-5 80.653 008 -5.190 008 -13.984 008 -10.540 008 4.972 008 2.546 008 18.340 008 36.085 008 38.857 008 6.991 008 4.938 008 -14.013 Number of Outliers 0 Sig. 000 .000 000 000 .000 000 012 000 000 .000 000 000 .000 Lag 24- 23 22 21- 20 19 18 17 16 15 13 12 11- 10 9 8 -1.0 -0.5 Residual ACF 10--0- O 0 0.0 1.0 0.5 -1.0 Residual Figure 1.2: Model 1 -0.5 Residual PACF 0 0.0 0.5 1.0 Hotel Occupancy - Model_1 1200 1000 800 Ada -009 400 FOCT 1990 MAY 1990 DEC 1989 JUL 1989 FEB 1989 SEP 1988 APR 1988 NOV 1987 JUN 1987 JAN 1987 FAUG 1986 MAR 1986 FOCT 1985 MAY 1985 DEC 1984 JUL 1984 FEB 1984 SEP 1983 APR 1983 NOV 1982 JUN 1982 JAN 1982 AUG 1981 MAR 1981 FOCT 1980 MAY 1980 DEC 1979 JUL 1979 FEB 1979 SEP 1978 APR 1978 NOV 1977 JUN 1977 JAN 1977 Date Figure 1.1: Monthly hotel room occupancy in the USA from Jan 1977 to Dec 1990 Hotel Occupancy Model 1 Hotel Occupancy Time $1 $2 S3 S4 $5 S6 S7 $8 S9 $10 $11 Model Hotel Occupancy- Model 1 Natural Log No Transformation No Transformation No Transformation No Transformation. No Transformation. No Transformation No Transformation No Transformation No Transformation No Transformation No Transformation No Transformation Number of Predictors ARIMA Model Parameters Constant Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator Numerator 12 Model Statistics Model Fit statistics. Stationary R- squared 989 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Lag 0 Ljung-Box Q(18) DF Statistics 96.328 Estimate 6.288 18 003 -042 -112 -084 040 020 147 289 311 056 040 -112 Sig. .000 SE t 006 978.262 3.379E-5 80.653 008 -5.190 008 -13.984 008 -10.540 008 4.972 008 2.546 008 18.340 008 36.085 008 38.857 008 6.991 008 4.938 008 -14.013 Number of Outliers 0 Sig. 000 .000 000 000 .000 000 012 000 000 .000 000 000 .000 Lag 24- 23 22 21- 20 19 18 17 16 15 13 12 11- 10 9 8 -1.0 -0.5 Residual ACF 10--0- O 0 0.0 1.0 0.5 -1.0 Residual Figure 1.2: Model 1 -0.5 Residual PACF 0 0.0 0.5 1.0 Hotel Occupancy - Model_1