a. Get a time series plot, SACF, and SPACF for the data. Do the plots indicate that the series is stationaryandnon-seasonal? Explain.

b. Get the 1stdifference (d1) of the series. Dothe time series, SACF, and SPACF plots for d1 indicate that the series is stationary?Explain.

c. What type of tentative ARMA model would you choose for the transformed data based on SACF and SPACF of the transformed series? Andwhy?

d.Use MA(1) model as the tentative model to fit the transformed data.Write down the model with assumptions and algebraically expand this model and express Yt as a function of past time series values, constant, and error terms.

e.Test the significant of constant and make the decision about whether to include the constant term. Estimate the model parameter(s).

f. Find forecast value for period 111 to 113 manually and compare your answers with SPSS output. If you are given the observationY111=6.0051 Update your forecast for period 112 to 113.

g. Use AR(1) model as the tentative model to fit the transformed data. Estimate the model parameter(s). Find forecast value for period 111 to 113. If you are given the observationY111=6.0051. Update your forecast for period 112.

data:

3.7136	1
3.6636	2
3.912	3
3.6889	4
3.7612	5
3.6376	6
3.7842	7
3.5553	8
3.6636	9
3.5553	10
3.3673	11
3.8918	12
3.912	13
4.0775	14
4.1431	15
3.4657	16
3.6636	17
3.8501	18
3.9703	19
4.0943	20
4.0431	21
3.9512	22
4.2485	23
4.4998	24
4.3041	25
4.1271	26
4.0073	27
4.4308	28
4.5433	29
4.2485	30
4.6821	31
4.9345	32
4.7875	33
4.5747	34
4.8363	35
5.0039	36
5.0626	37
4.8203	38
4.9416	39
4.6913	40
4.7362	41
4.3438	42
4.7875	43
4.8903	44
4.7005	45
4.5218	46
4.5747	47
4.3567	48
4.5951	49
4.6728	50
4.7185	51
4.4998	52
4.585	53
4.8283	54
5.0434	55
5.247	56
5.4638	57
5.2417	58
5.1591	59
5.1818	60
4.9127	61
5.0814	62
5.1417	63
5.0039	64
5.2149	65
5.0434	66
5.6204	67
5.4116	68
5.3613	69
5.6312	70
5.591	71
5.6595	72
5.4723	73
5.3613	74
5.5491	75
5.6802	76
5.3566	77
5.5053	78
5.8665	79
5.826	80
5.7301	81
5.5094	82
5.5491	83
5.7746	84
5.6971	85
5.6095	86
5.743	87
5.5175	88
5.656	89
5.6312	90
5.7333	91
5.994	92
5.7333	93
5.793	94
5.8665	95
5.8693	96
5.79	97
5.7807	98
5.6525	99
5.4931	100
5.4848	101
5.6595	102
5.8721	103
6.1312	104
5.8972	105
6.1883	106
6.1137	107
5.9687	108
6.2146	109
6.1115	110