Forecasting a series one date ahead

[Zankawa]

Dear Tom Doan,
I am trying to use an extrapolation method to forecast a series one date ahead in order to obtain the last value of the series for a GARCH BEKK model. I have attempted using exponential smoothing and ARIMA to forecast the value but I am not very familiar with any of the two methods. I wanted to ask if you could assist me on how to use any of these methods to obtain the value. I have pasted the data below, and I am forecasting the value for Jan-2011.
Thank you

Code: Select all

 Period	GSECI
Jan-91	67.69
Feb-91	66.03
Mar-91	63.68
Apr-91	61.43
May-91	59.42
Jun-91	59.71
Jul-91	59.50
Aug-91	59.26
Sep-91	58.75
Oct-91	68.90
Nov-91	62.38
Dec-91	64.22
Jan-92	67.20
Feb-92	68.81
Mar-92	66.00
Apr-92	63.54
May-92	61.56
Jun-92	60.72
Jul-92	65.63
Aug-92	70.21
Sep-92	71.86
Oct-92	72.31
Nov-92	71.31
Dec-92	66.47
Jan-93	73.03
Feb-93	84.63
Mar-93	79.44
Apr-93	82.89
May-93	84.71
Jun-93	87.36
Jul-93	91.20
Aug-93	100.01
Sep-93	103.22
Oct-93	109.37
Nov-93	120.93
Dec-93	131.32
Jan-94	138.07
Feb-94	145.94
Mar-94	204.70
Apr-94	290.12
May-94	324.90
Jun-94	310.87
Jul-94	299.62
Aug-94	291.29
Sep-94	296.18
Oct-94	303.14
Nov-94	300.56
Dec-94	296.86
Jan-95	298.48
Feb-95	298.98
Mar-95	297.63
Apr-95	310.04
May-95	315.28
Jun-95	307.34
Jul-95	310.57
Aug-95	312.95
Sep-95	308.53
Oct-95	317.16
Nov-95	320.51
Dec-95	318.03
Jan-96	312.45
Feb-96	326.10
Mar-96	330.95
Apr-96	349.98
May-96	349.90
Jun-96	360.75
Jul-96	365.66
Aug-96	373.45
Sep-96	383.21
Oct-96	373.64
Nov-96	367.40
Dec-96	360.34
Jan-97	356.60
Feb-97	355.63
Mar-97	362.17
Apr-97	365.74
May-97	381.58
Jun-97	385.27
Jul-97	385.11
Aug-97	403.94
Sep-97	427.78
Oct-97	470.42
Nov-97	499.34
Dec-97	500.71
Jan-98	526.95
Feb-98	591.61
Mar-98	736.92
Apr-98	1,053.61
May-98	1,125.33
Jun-98	935.43
Jul-98	992.88
Aug-98	1,004.58
Sep-98	943.60
Oct-98	825.64
Nov-98	786.94
Dec-98	827.79
Jan-99	878.49
Feb-99	881.03
Mar-99	834.19
Apr-99	823.10
May-99	819.16
Jun-99	800.43
Jul-99	791.79
Aug-99	785.82
Sep-99	770.54
Oct-99	762.45
Nov-99	752.61
Dec-99	741.37
Jan-00	739.43
Feb-00	742.00
Mar-00	754.25
Apr-00	820.24
May-00	820.44
Jun-00	816.15
Jul-00	821.06
Aug-00	820.92
Sep-00	850.35
Oct-00	855.75
Nov-00	855.68
Dec-00	863.31
Jan-01	859.66
Feb-01	862.02
Mar-01	895.46
Apr-01	897.26
May-01	896.80
Jun-01	909.03
Jul-01	941.57
Aug-01	949.65
Sep-01	953.34
Oct-01	959.99
Nov-01	958.52
Dec-01	958.14
Jan-02	956.41
Feb-02	963.84
Mar-02	996.03
Apr-02	1,026.31
May-02	1,072.87
Jun-02	1,185.38
Jul-02	1,243.67
Aug-02	1,281.01
Sep-02	1,308.27
Oct-02	1,331.67
Nov-02	1,353.14
Dec-02	1,377.65
Jan-03	1,416.82
Feb-03	1,462.01
Mar-03	1,592.55
Apr-03	1,718.51
May-03	1,815.16
Jun-03	1,967.87
Jul-03	2,206.35
Aug-03	2,431.90
Sep-03	2,603.26
Oct-03	2,792.59
Nov-03	3,057.60
Dec-03	3,421.26
Jan-04	3,654.62
Feb-04	4,146.25
Mar-04	5,256.73
Apr-04	6,230.76
May-04	6,743.18
Jun-04	6,964.84
Jul-04	7,092.48
Aug-04	7,741.31
Sep-04	7,089.17
Oct-04	6,996.18
Nov-04	6,838.28
Dec-04	6,779.01
Jan-05	6,855.63
Feb-05	6,820.77
Mar-05	6,577.69
Apr-05	6,305.70
May-05	6,065.66
Jun-05	6,003.22
Jul-05	5,312.69
Aug-05	4,855.47
Sep-05	4,880.92
Oct-05	4,893.13
Nov-05	4,896.79
Dec-05	4,784.90
Jan-06	4,731.62
Feb-06	4,739.34
Mar-06	4,758.28
Apr-06	4,780.15
May-06	4,807.33
Jun-06	4,860.40
Jul-06	4,878.50
Aug-06	4,906.18
Sep-06	4,950.44
Oct-06	4,974.89
Nov-06	5,002.29
Dec-06	5,021.32
Jan-07	5,028.87
Feb-07	5,051.00
Mar-07	5,089.42
Apr-07	5,145.33
May-07	5,184.89
Jun-07	5,280.90
Jul-07	5,365.85
Aug-07	5,467.68
Sep-07	5,629.87
Oct-07	5,766.73
Nov-07	5,930.36
Dec-07	6,487.48
Jan-08	6,668.25
Feb-08	6,859.27
Mar-08	7,260.29
Apr-08	8,719.04
May-08	9,583.17
Jun-08	10,146.02
Jul-08	10,535.26
Aug-08	10,665.03
Sep-08	10,882.70
Oct-08	10,858.61
Nov-08	10,615.86
Dec-08	10,473.62
Jan-09	10,342.70
Feb-09	9,997.79
Mar-09	9,591.53
Apr-09	8,980.21
May-09	8,269.90
Jun-09	6,143.88
Jul-09	5,364.78
Aug-09	5,287.17
Sep-09	6,429.10
Oct-09	5,982.39
Nov-09	5,403.63
Dec-09	5,378.85
Jan-10	5,545.42
Feb-10	5,633.79
Mar-10	5,788.63
Apr-10	6,256.21
May-10	6,998.68
Jun-10	6,721.06
Jul-10	6,361.90
Aug-10	6,483.59
Sep-10	6,754.55
Oct-10	6,809.34
Nov-10	6,882.74
Dec-10	7,165.17
Jan-11

[TomDoan]

I'm confused about what you're asking. What do exponential smoothing or ARIMA models have to do with a GARCH BEKK?

[Zankawa]

Sorry, I mean that I am trying to obtain the last value of the series by extrapolating method as the value is missing. The series is going to be used with other series to estimate a GARCH BEKK, but before estimating the GARCH, I need to obtain all the values for the series for the sample period. The other series have all the values but the last value of this particular series is missing and I am trying to obtain that value by extrapolating possibly using exponential smoothing.
I hope the question is clear now.

[TomDoan]

Wouldn't it make more sense to just drop the one complete observation? The whole point of a GARCH model is to deal with joint behavior of the residuals and any "patch" procedure is going to replace that data point with what would give you in effect a zero residual.

Your biggest problem isn't one missing observation. Your data has several huge structural breaks. You can't just fit a GARCH model to that and expect reasonable results.

[Zankawa]

Thank you so much for this reply. I will be very grateful if you could offer some suggestions about how I can deal with the structural breaks in the data before fitting the series in a GARCH.
Thank you

[Zankawa]

I have tested the series for a unit root and the series are all I(1). Therefore, I have taken their first differences before fitting them into the GARCH. Will this solve the problem of the structural breaks in the series?
Thank you

[TomDoan]

The best way to "solve" the problem is to understand the source of it. This is your data, so you should know why there are those rather sudden changes. And, no, in general, differencing has no effect on something like this. It simply changes it from a sudden jump in level to a massive spike in the difference.