(a)Explain the four steps of Box-Jenkin’s methods of forecasting. (b)Using Box-J
ID: 1159851 • Letter: #
Question
(a)Explain the four steps of Box-Jenkin’s methods of forecasting.
(b)Using Box-Jenkin’s four-step method, forecast the US quarterly GDP for the second quarter of 2015.
observation_date
GDP (billion $)
1947-01-01
1934.5
1947-04-01
1932.3
1947-07-01
1930.3
1947-10-01
1960.7
1948-01-01
1989.5
1948-04-01
2021.9
1948-07-01
2033.2
1948-10-01
2035.3
1949-01-01
2007.5
1949-04-01
2000.8
1949-07-01
2022.8
1949-10-01
2004.7
1950-01-01
2084.6
1950-04-01
2147.6
1950-07-01
2230.4
1950-10-01
2273.4
1951-01-01
2304.5
1951-04-01
2344.5
1951-07-01
2392.8
1951-10-01
2398.1
1952-01-01
2423.5
1952-04-01
2428.5
1952-07-01
2446.1
1952-10-01
2526.4
1953-01-01
2573.4
1953-04-01
2593.5
1953-07-01
2578.9
1953-10-01
2539.8
1954-01-01
2528.0
1954-04-01
2530.7
1954-07-01
2559.4
1954-10-01
2609.3
1955-01-01
2683.8
1955-04-01
2727.5
1955-07-01
2764.1
1955-10-01
2780.8
1956-01-01
2770.0
1956-04-01
2792.9
1956-07-01
2790.6
1956-10-01
2836.2
1957-01-01
2854.5
1957-04-01
2848.2
1957-07-01
2875.9
1957-10-01
2846.4
1958-01-01
2772.7
1958-04-01
2790.9
1958-07-01
2855.5
1958-10-01
2922.3
1959-01-01
2976.6
1959-04-01
3049.0
1959-07-01
3043.1
1959-10-01
3055.1
1960-01-01
3123.2
1960-04-01
3111.3
1960-07-01
3119.1
1960-10-01
3081.3
1961-01-01
3102.3
1961-04-01
3159.9
1961-07-01
3212.6
1961-10-01
3277.7
1962-01-01
3336.8
1962-04-01
3372.7
1962-07-01
3404.8
1962-10-01
3418.0
1963-01-01
3456.1
1963-04-01
3501.1
1963-07-01
3569.5
1963-10-01
3595.0
1964-01-01
3672.7
1964-04-01
3716.4
1964-07-01
3766.9
1964-10-01
3780.2
1965-01-01
3873.5
1965-04-01
3926.4
1965-07-01
4006.2
1965-10-01
4100.6
1966-01-01
4201.9
1966-04-01
4219.1
1966-07-01
4249.2
1966-10-01
4285.6
1967-01-01
4324.9
1967-04-01
4328.7
1967-07-01
4366.1
1967-10-01
4401.2
1968-01-01
4490.6
1968-04-01
4566.4
1968-07-01
4599.3
1968-10-01
4619.8
1969-01-01
4691.6
1969-04-01
4706.7
1969-07-01
4736.1
1969-10-01
4715.5
1970-01-01
4707.1
1970-04-01
4715.4
1970-07-01
4757.2
1970-10-01
4708.3
1971-01-01
4834.3
1971-04-01
4861.9
1971-07-01
4900.0
1971-10-01
4914.3
1972-01-01
5002.4
1972-04-01
5118.3
1972-07-01
5165.4
1972-10-01
5251.2
1973-01-01
5380.5
1973-04-01
5441.5
1973-07-01
5411.9
1973-10-01
5462.4
1974-01-01
5417.0
1974-04-01
5431.3
1974-07-01
5378.7
1974-10-01
5357.2
1975-01-01
5292.4
1975-04-01
5333.2
1975-07-01
5421.4
1975-10-01
5494.4
1976-01-01
5618.5
1976-04-01
5661.0
1976-07-01
5689.8
1976-10-01
5732.5
1977-01-01
5799.2
1977-04-01
5913.0
1977-07-01
6017.6
1977-10-01
6018.2
1978-01-01
6039.2
1978-04-01
6274.0
1978-07-01
6335.3
1978-10-01
6420.3
1979-01-01
6433.0
1979-04-01
6440.8
1979-07-01
6487.1
1979-10-01
6503.9
1980-01-01
6524.9
1980-04-01
6392.6
1980-07-01
6382.9
1980-10-01
6501.2
1981-01-01
6635.7
1981-04-01
6587.3
1981-07-01
6662.9
1981-10-01
6585.1
1982-01-01
6475.0
1982-04-01
6510.2
1982-07-01
6486.8
1982-10-01
6493.1
1983-01-01
6578.2
1983-04-01
6728.3
1983-07-01
6860.0
1983-10-01
7001.5
1984-01-01
7140.6
1984-04-01
7266.0
1984-07-01
7337.5
1984-10-01
7396.0
1985-01-01
7469.5
1985-04-01
7537.9
1985-07-01
7655.2
1985-10-01
7712.6
1986-01-01
7784.1
1986-04-01
7819.8
1986-07-01
7898.6
1986-10-01
7939.5
1987-01-01
7995.0
1987-04-01
8084.7
1987-07-01
8158.0
1987-10-01
8292.7
1988-01-01
8339.3
1988-04-01
8449.5
1988-07-01
8498.3
1988-10-01
8610.9
1989-01-01
8697.7
1989-04-01
8766.1
1989-07-01
8831.5
1989-10-01
8850.2
1990-01-01
8947.1
1990-04-01
8981.7
1990-07-01
8983.9
1990-10-01
8907.4
1991-01-01
8865.6
1991-04-01
8934.4
1991-07-01
8977.3
1991-10-01
9016.4
1992-01-01
9123.0
1992-04-01
9223.5
1992-07-01
9313.2
1992-10-01
9406.5
1993-01-01
9424.1
1993-04-01
9480.1
1993-07-01
9526.3
1993-10-01
9653.5
1994-01-01
9748.2
1994-04-01
9881.4
1994-07-01
9939.7
1994-10-01
10052.5
1995-01-01
10086.9
1995-04-01
10122.1
1995-07-01
10208.8
1995-10-01
10281.2
1996-01-01
10348.7
1996-04-01
10529.4
1996-07-01
10626.8
1996-10-01
10739.1
1997-01-01
10820.9
1997-04-01
10984.2
1997-07-01
11124.0
1997-10-01
11210.3
1998-01-01
11321.2
1998-04-01
11431.0
1998-07-01
11580.6
1998-10-01
11770.7
1999-01-01
11864.7
1999-04-01
11962.5
1999-07-01
12113.1
1999-10-01
12323.3
2000-01-01
12359.1
2000-04-01
12592.5
2000-07-01
12607.7
2000-10-01
12679.3
2001-01-01
12643.3
2001-04-01
12710.3
2001-07-01
12670.1
2001-10-01
12705.3
2002-01-01
12822.3
2002-04-01
12893.0
2002-07-01
12955.8
2002-10-01
12964.0
2003-01-01
13031.2
2003-04-01
13152.1
2003-07-01
13372.4
2003-10-01
13528.7
2004-01-01
13606.5
2004-04-01
13706.2
2004-07-01
13830.8
2004-10-01
13950.4
2005-01-01
14099.1
2005-04-01
14172.7
2005-07-01
14291.8
2005-10-01
14373.4
2006-01-01
14546.1
2006-04-01
14589.6
2006-07-01
14602.6
2006-10-01
14716.9
2007-01-01
14726.0
2007-04-01
14838.7
2007-07-01
14938.5
2007-10-01
14991.8
2008-01-01
14889.5
2008-04-01
14963.4
2008-07-01
14891.6
2008-10-01
14577.0
2009-01-01
14375.0
2009-04-01
14355.6
2009-07-01
14402.5
2009-10-01
14541.9
2010-01-01
14604.8
2010-04-01
14745.9
2010-07-01
14845.5
2010-10-01
14939.0
2011-01-01
14881.3
2011-04-01
14989.6
2011-07-01
15021.1
2011-10-01
15190.3
2012-01-01
15275.0
2012-04-01
15336.7
2012-07-01
15431.3
2012-10-01
15433.7
2013-01-01
15538.4
2013-04-01
15606.6
2013-07-01
15779.9
2013-10-01
15916.2
2014-01-01
15831.7
2014-04-01
16010.4
2014-07-01
16205.6
2014-10-01
16294.7
2015-01-01
16264.1
observation_date
GDP (billion $)
1947-01-01
1934.5
1947-04-01
1932.3
1947-07-01
1930.3
1947-10-01
1960.7
1948-01-01
1989.5
1948-04-01
2021.9
1948-07-01
2033.2
1948-10-01
2035.3
1949-01-01
2007.5
1949-04-01
2000.8
1949-07-01
2022.8
1949-10-01
2004.7
1950-01-01
2084.6
1950-04-01
2147.6
1950-07-01
2230.4
1950-10-01
2273.4
1951-01-01
2304.5
1951-04-01
2344.5
1951-07-01
2392.8
1951-10-01
2398.1
1952-01-01
2423.5
1952-04-01
2428.5
1952-07-01
2446.1
1952-10-01
2526.4
1953-01-01
2573.4
1953-04-01
2593.5
1953-07-01
2578.9
1953-10-01
2539.8
1954-01-01
2528.0
1954-04-01
2530.7
1954-07-01
2559.4
1954-10-01
2609.3
1955-01-01
2683.8
1955-04-01
2727.5
1955-07-01
2764.1
1955-10-01
2780.8
1956-01-01
2770.0
1956-04-01
2792.9
1956-07-01
2790.6
1956-10-01
2836.2
1957-01-01
2854.5
1957-04-01
2848.2
1957-07-01
2875.9
1957-10-01
2846.4
1958-01-01
2772.7
1958-04-01
2790.9
1958-07-01
2855.5
1958-10-01
2922.3
1959-01-01
2976.6
1959-04-01
3049.0
1959-07-01
3043.1
1959-10-01
3055.1
1960-01-01
3123.2
1960-04-01
3111.3
1960-07-01
3119.1
1960-10-01
3081.3
1961-01-01
3102.3
1961-04-01
3159.9
1961-07-01
3212.6
1961-10-01
3277.7
1962-01-01
3336.8
1962-04-01
3372.7
1962-07-01
3404.8
1962-10-01
3418.0
1963-01-01
3456.1
1963-04-01
3501.1
1963-07-01
3569.5
1963-10-01
3595.0
1964-01-01
3672.7
1964-04-01
3716.4
1964-07-01
3766.9
1964-10-01
3780.2
1965-01-01
3873.5
1965-04-01
3926.4
1965-07-01
4006.2
1965-10-01
4100.6
1966-01-01
4201.9
1966-04-01
4219.1
1966-07-01
4249.2
1966-10-01
4285.6
1967-01-01
4324.9
1967-04-01
4328.7
1967-07-01
4366.1
1967-10-01
4401.2
1968-01-01
4490.6
1968-04-01
4566.4
1968-07-01
4599.3
1968-10-01
4619.8
1969-01-01
4691.6
1969-04-01
4706.7
1969-07-01
4736.1
1969-10-01
4715.5
1970-01-01
4707.1
1970-04-01
4715.4
1970-07-01
4757.2
1970-10-01
4708.3
1971-01-01
4834.3
1971-04-01
4861.9
1971-07-01
4900.0
1971-10-01
4914.3
1972-01-01
5002.4
1972-04-01
5118.3
1972-07-01
5165.4
1972-10-01
5251.2
1973-01-01
5380.5
1973-04-01
5441.5
1973-07-01
5411.9
1973-10-01
5462.4
1974-01-01
5417.0
1974-04-01
5431.3
1974-07-01
5378.7
1974-10-01
5357.2
1975-01-01
5292.4
1975-04-01
5333.2
1975-07-01
5421.4
1975-10-01
5494.4
1976-01-01
5618.5
1976-04-01
5661.0
1976-07-01
5689.8
1976-10-01
5732.5
1977-01-01
5799.2
1977-04-01
5913.0
1977-07-01
6017.6
1977-10-01
6018.2
1978-01-01
6039.2
1978-04-01
6274.0
1978-07-01
6335.3
1978-10-01
6420.3
1979-01-01
6433.0
1979-04-01
6440.8
1979-07-01
6487.1
1979-10-01
6503.9
1980-01-01
6524.9
1980-04-01
6392.6
1980-07-01
6382.9
1980-10-01
6501.2
1981-01-01
6635.7
1981-04-01
6587.3
1981-07-01
6662.9
1981-10-01
6585.1
1982-01-01
6475.0
1982-04-01
6510.2
1982-07-01
6486.8
1982-10-01
6493.1
1983-01-01
6578.2
1983-04-01
6728.3
1983-07-01
6860.0
1983-10-01
7001.5
1984-01-01
7140.6
1984-04-01
7266.0
1984-07-01
7337.5
1984-10-01
7396.0
1985-01-01
7469.5
1985-04-01
7537.9
1985-07-01
7655.2
1985-10-01
7712.6
1986-01-01
7784.1
1986-04-01
7819.8
1986-07-01
7898.6
1986-10-01
7939.5
1987-01-01
7995.0
1987-04-01
8084.7
1987-07-01
8158.0
1987-10-01
8292.7
1988-01-01
8339.3
1988-04-01
8449.5
1988-07-01
8498.3
1988-10-01
8610.9
1989-01-01
8697.7
1989-04-01
8766.1
1989-07-01
8831.5
1989-10-01
8850.2
1990-01-01
8947.1
1990-04-01
8981.7
1990-07-01
8983.9
1990-10-01
8907.4
1991-01-01
8865.6
1991-04-01
8934.4
1991-07-01
8977.3
1991-10-01
9016.4
1992-01-01
9123.0
1992-04-01
9223.5
1992-07-01
9313.2
1992-10-01
9406.5
1993-01-01
9424.1
1993-04-01
9480.1
1993-07-01
9526.3
1993-10-01
9653.5
1994-01-01
9748.2
1994-04-01
9881.4
1994-07-01
9939.7
1994-10-01
10052.5
1995-01-01
10086.9
1995-04-01
10122.1
1995-07-01
10208.8
1995-10-01
10281.2
1996-01-01
10348.7
1996-04-01
10529.4
1996-07-01
10626.8
1996-10-01
10739.1
1997-01-01
10820.9
1997-04-01
10984.2
1997-07-01
11124.0
1997-10-01
11210.3
1998-01-01
11321.2
1998-04-01
11431.0
1998-07-01
11580.6
1998-10-01
11770.7
1999-01-01
11864.7
1999-04-01
11962.5
1999-07-01
12113.1
1999-10-01
12323.3
2000-01-01
12359.1
2000-04-01
12592.5
2000-07-01
12607.7
2000-10-01
12679.3
2001-01-01
12643.3
2001-04-01
12710.3
2001-07-01
12670.1
2001-10-01
12705.3
2002-01-01
12822.3
2002-04-01
12893.0
2002-07-01
12955.8
2002-10-01
12964.0
2003-01-01
13031.2
2003-04-01
13152.1
2003-07-01
13372.4
2003-10-01
13528.7
2004-01-01
13606.5
2004-04-01
13706.2
2004-07-01
13830.8
2004-10-01
13950.4
2005-01-01
14099.1
2005-04-01
14172.7
2005-07-01
14291.8
2005-10-01
14373.4
2006-01-01
14546.1
2006-04-01
14589.6
2006-07-01
14602.6
2006-10-01
14716.9
2007-01-01
14726.0
2007-04-01
14838.7
2007-07-01
14938.5
2007-10-01
14991.8
2008-01-01
14889.5
2008-04-01
14963.4
2008-07-01
14891.6
2008-10-01
14577.0
2009-01-01
14375.0
2009-04-01
14355.6
2009-07-01
14402.5
2009-10-01
14541.9
2010-01-01
14604.8
2010-04-01
14745.9
2010-07-01
14845.5
2010-10-01
14939.0
2011-01-01
14881.3
2011-04-01
14989.6
2011-07-01
15021.1
2011-10-01
15190.3
2012-01-01
15275.0
2012-04-01
15336.7
2012-07-01
15431.3
2012-10-01
15433.7
2013-01-01
15538.4
2013-04-01
15606.6
2013-07-01
15779.9
2013-10-01
15916.2
2014-01-01
15831.7
2014-04-01
16010.4
2014-07-01
16205.6
2014-10-01
16294.7
2015-01-01
16264.1
Explanation / Answer
(a) The Four-steps of Box-Jenkins method are:
* Identification - A simple Auto-Regressive Integrated Moving Average (ARIMA) model is selectd using the given dataset, auto-correlation, partial auto-correlation and other informations. Then the values of p, d and q are estimated. This method is the only one which differences the trend unlike the models which removes the trend. p value determines the order of auto-correlation. d values determines the level of differentiation. q value determines the order of moving average.
* Estimation - Once the values p, d and q are estimated, the parameters are then estimated by Maximum-Likelihood method. This is an intensive and iterative method. So it takes time to provide solution. It is outlined in Box-Jenkins method.
* Diagnostic Checking - Once a model is fit then it is the time for diagnostic checking. It is done by analysis the auto-correlation(AC) and partial auto-correlation(PAC) plots of the residuals. If any large value i s obtained then the values of p, d and q are adjusted and the model is re-estimated. This is done till there is no large values of Acs and PACs.
* Forecasting - Once th emodel is properly estimated then the future values based on the given dataset is forecasted.
(b) This is a large dataset of 273 rows. It is not possible to calculate manually. It is also not allowed to any report from other tools or softwares. But it can be forecasted using any statistical tools/softwares. However a guidelne to do so is given below:
* Plot a graph using the given dataset and check for presence of any trends. If it is present, differentiate it. Unit root test can be used. Over-differentiation should be avoided. the d values should be obtained.
* The best model should be used to get a summarized report of the data. Acs and PACs should be analysed from the report using ACF and PACF. The p and q values should be obtained properly.
*Then estimation is done to reduce error terms.
*Diagnostic Checking is to check the residuals errors and overfiitting. Both these result to wrong forecasting.
*Once the model is estimated properly then the value should be forecasted.
Box-Jenkins method is provide in the statistical softwares these days.
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