Question

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	15107.3

Answer 1

I made a program of Box-Jenkins ARIMA model for forecasting GDP for the second quarter of 2015 as below:

rm(list=ls())
data=read.csv(file.choose())
GDP=data[,2]
library(timeSeries)
GDP=ts(GDP,start=c(1947,1),frequency=4)
plot(GDP)
library(tseries)
adf.test(GDP) # for stationarity
GDP1=diff(GDP)
adf.test(GDP1)
#d=1
acf(GDP1)
#q=2
pacf(GDP1)
#p=1
#Apply ARIMA(1,1,2)

fit<-arima(GDP, order=c(1,1,2))
library(forecast)
pred=forecast(fit,h=1)

final output is : ​

Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
2015 Q2 14481.23 14356.27 14606.2 14290.12 14672.35