Go to http://fred.stlouisfed.org, search for real gross domestic product, and do

Question

Go to http://fred.stlouisfed.org, search for real gross domestic product, and download the quarterly data, in billions of chained 2009 dollars, seasonally adjusted annual rate Excel file. Once you reach the Real Gross Domestic Product graph page, the download button will be in the upper right corner of the screen. Be sure to give through explanations and show your work throughout.

1. Test, at the 95% confidence level, if the level of real GDP is stationary. Be sure to state your null and alternative hypotheses. What do you conclude from this test?

Data:

observation_date GDPC1 Percent Change       1947-01-01 1934.5 1947-04-01 1932.3 -0.1 1947-07-01 1930.3 -0.1 1947-10-01 1960.7 1.6 1948-01-01 1989.5 1.5 1948-04-01 2021.9 1.6 1948-07-01 2033.2 0.6 1948-10-01 2035.3 0.1 1949-01-01 2007.5 -1.4 1949-04-01 2000.8 -0.3 1949-07-01 2022.8 1.1 1949-10-01 2004.7 -0.9 1950-01-01 2084.6 4.0 1950-04-01 2147.6 3.1 1950-07-01 2230.4 3.9 1950-10-01 2273.4 1.9 1951-01-01 2304.5 1.4 1951-04-01 2344.5 1.7 1951-07-01 2392.8 2.1 1951-10-01 2398.1 0.2 1952-01-01 2423.5 1.1 1952-04-01 2428.5 0.2 1952-07-01 2446.1 0.7 1952-10-01 2526.4 3.3 1953-01-01 2573.4 1.9 1953-04-01 2593.5 0.8 1953-07-01 2578.9 -0.6 1953-10-01 2539.8 -1.5 1954-01-01 2528.0 -0.5 1954-04-01 2530.7 0.1 1954-07-01 2559.4 1.1 1954-10-01 2609.3 1.9 1955-01-01 2683.8 2.9 1955-04-01 2727.5 1.6 1955-07-01 2764.1 1.3 1955-10-01 2780.8 0.6 1956-01-01 2770.0 -0.4 1956-04-01 2792.9 0.8 1956-07-01 2790.6 0.0 1956-10-01 2836.2 1.6 1957-01-01 2854.5 0.6 1957-04-01 2848.2 -0.2 1957-07-01 2875.9 1.0 1957-10-01 2846.4 -1.0 1958-01-01 2772.7 -2.6 1958-04-01 2790.9 0.7 1958-07-01 2855.5 2.3 1958-10-01 2922.3 2.3 1959-01-01 2976.6 1.9 1959-04-01 3049.0 2.4 1959-07-01 3043.1 -0.2 1959-10-01 3055.1 0.4 1960-01-01 3123.2 2.2 1960-04-01 3111.3 -0.4 1960-07-01 3119.1 0.3 1960-10-01 3081.3 -1.2 1961-01-01 3102.3 0.7 1961-04-01 3159.9 1.9 1961-07-01 3212.6 1.7 1961-10-01 3277.7 2.0 1962-01-01 3336.8 1.8 1962-04-01 3372.7 1.1 1962-07-01 3404.8 1.0 1962-10-01 3418.0 0.4 1963-01-01 3456.1 1.1 1963-04-01 3501.1 1.3 1963-07-01 3569.5 2.0 1963-10-01 3595.0 0.7 1964-01-01 3672.7 2.2 1964-04-01 3716.4 1.2 1964-07-01 3766.9 1.4 1964-10-01 3780.2 0.4 1965-01-01 3873.5 2.5 1965-04-01 3926.4 1.4 1965-07-01 4006.2 2.0 1965-10-01 4100.6 2.4 1966-01-01 4201.9 2.5 1966-04-01 4219.1 0.4 1966-07-01 4249.2 0.7 1966-10-01 4285.6 0.9 1967-01-01 4324.9 0.9 1967-04-01 4328.7 0.1 1967-07-01 4366.1 0.9 1967-10-01 4401.2 0.8 1968-01-01 4490.6 2.0 1968-04-01 4566.4 1.7 1968-07-01 4599.3 0.7 1968-10-01 4619.8 0.5 1969-01-01 4691.6 1.6 1969-04-01 4706.7 0.3 1969-07-01 4736.1 0.6 1969-10-01 4715.5 -0.4 1970-01-01 4707.1 -0.2 1970-04-01 4715.4 0.2 1970-07-01 4757.2 0.9 1970-10-01 4708.3 -1.0 1971-01-01 4834.3 2.7 1971-04-01 4861.9 0.6 1971-07-01 4900.0 0.8 1971-10-01 4914.3 0.3 1972-01-01 5002.4 1.8 1972-04-01 5118.3 2.3 1972-07-01 5165.4 0.9 1972-10-01 5251.2 1.7 1973-01-01 5380.5 2.5 1973-04-01 5441.5 1.1 1973-07-01 5411.9 -0.5 1973-10-01 5462.4 0.9 1974-01-01 5417.0 -0.8 1974-04-01 5431.3 0.3 1974-07-01 5378.7 -1.0 1974-10-01 5357.2 -0.4 1975-01-01 5292.4 -1.2 1975-04-01 5333.2 0.8 1975-07-01 5421.4 1.7 1975-10-01 5494.4 1.4 1976-01-01 5618.5 2.3 1976-04-01 5661.0 0.8 1976-07-01 5689.8 0.5 1976-10-01 5732.5 0.8 1977-01-01 5799.2 1.2 1977-04-01 5913.0 2.0 1977-07-01 6017.6 1.8 1977-10-01 6018.2 0.0 1978-01-01 6039.2 0.4 1978-04-01 6274.0 3.9 1978-07-01 6335.3 1.0 1978-10-01 6420.3 1.3 1979-01-01 6433.0 0.2 1979-04-01 6440.8 0.1 1979-07-01 6487.1 0.7 1979-10-01 6503.9 0.3 1980-01-01 6524.9 0.3 1980-04-01 6392.6 -2.0 1980-07-01 6382.9 -0.2 1980-10-01 6501.2 1.9 1981-01-01 6635.7 2.1 1981-04-01 6587.3 -0.7 1981-07-01 6662.9 1.2 1981-10-01 6585.1 -0.1 1982-01-01 6475.0 -1.7 1982-04-01 6510.2 0.5 1982-07-01 6486.8 -0.4 1982-10-01 6493.1 0.1 1983-01-01 6578.2 1.3 1983-04-01 6728.3 2.3 1983-07-01 6860.0 2.0 1983-10-01 7001.5 2.1 1984-01-01 7140.6 2.0 1984-04-01 7266.0 1.8 1984-07-01 7337.5 1.0 1984-10-01 7396.0 0.8 1985-01-01 7469.5 1.0 1985-04-01 7537.9 0.9 1985-07-01 7655.2 1.6 1985-10-01 7712.6 0.8 1986-01-01 7784.1 0.9 1986-04-01 7819.8 0.5 1986-07-01 7898.6 1.0 1986-10-01 7939.5 0.5 1987-01-01 7995.0 0.7 1987-04-01 8084.7 1.1 1987-07-01 8158.0 0.9 1987-10-01 8292.7 1.7 1988-01-01 8339.3 0.6 1988-04-01 8449.5 1.3 1988-07-01 8498.3 0.6 1988-10-01 8610.9 1.3 1989-01-01 8697.7 1.0 1989-04-01 8766.1 0.8 1989-07-01 8831.5 0.8 1989-10-01 8850.2 0.2 1990-01-01 8947.1 1.1 1990-04-01 8981.7 0.4 1990-07-01 8983.9 0.0 1990-10-01 8907.4 -0.9 1991-01-01 8865.6 -0.5 1991-04-01 8934.4 0.8 1991-07-01 8977.3 0.5 1991-10-01 9016.4 0.4 1992-01-01 9123.0 1.2 1992-04-01 9223.5 1.1 1992-07-01 9313.2 1.0 1992-10-01 9406.5 1.0 1993-01-01 9424.1 0.2 1993-04-01 9480.1 0.6 1993-07-01 9526.3 0.5 1993-10-01 9653.5 1.3 1994-01-01 9748.2 1.0 1994-04-01 9881.4 1.4 1994-07-01 9939.7 0.6 1994-10-01 10052.5 1.1 1995-01-01 10086.9 0.3 1995-04-01 10122.1 0.4 1995-07-01 10208.8 0.9 1995-10-01 10281.2 0.7 1996-01-01 10348.7 0.7 1996-04-01 10529.4 1.8 1996-07-01 10626.8 0.9 1996-10-01 10739.1 1.1 1997-01-01 10820.9 0.8 1997-04-01 10984.2 1.5 1997-07-01 11124.0 1.3 1997-10-01 11210.3 0.8 1998-01-01 11321.2 1.0 1998-04-01 11431.0 1.0 1998-07-01 11580.6 1.3 1998-10-01 11770.7 0.6 1999-01-01 11864.7 0.8 1999-04-01 11962.5 0.8 1999-07-01 12113.1 0.1 1999-10-01 12323.3 1.7 2000-01-01 12359.1 0.3 2000-04-01 12592.5 1.9 2000-07-01 12607.7 0.1 2000-10-01 12679.3 0.6 2001-01-01 12643.3 -0.3 2001-04-01 12710.3 0.5 2001-07-01 12670.1 -0.3 2001-10-01 12705.3 0.3 2002-01-01 12822.3 0.9 2002-04-01 12893.0 0.6 2002-07-01 12955.8 0.5 2002-10-01 12964.0 0.1 2003-01-01 13031.2 0.5 2003-04-01 13152.1 0.9 2003-07-01 13372.4 1.7 2003-10-01 13528.7 1.2 2004-01-01 13606.5 0.6 2004-04-01 13706.2 0.7 2004-07-01 13830.8 0.9 2004-10-01 13950.4 0.9 2005-01-01 14099.1 1.1 2005-04-01 14172.7 0.5 2005-07-01 14291.8 0.8 2005-10-01 14373.4 0.6 2006-01-01 14546.1 1.2 2006-04-01 14589.6 0.3 2006-07-01 14602.6 0.1 2006-10-01 14716.9 0.8 2007-01-01 14726.0 0.1 2007-04-01 14838.7 0.8 2007-07-01 14938.5 0.7 2007-10-01 14991.8 0.4 2008-01-01 14889.5 -0.7 2008-04-01 14963.4 0.5 2008-07-01 14891.6 -0.5 2008-10-01 14577.0 -2.1 2009-01-01 14375.0 -1.4 2009-04-01 14355.6 -0.1 2009-07-01 14402.5 0.3 2009-10-01 14541.9 1.0 2010-01-01 14604.8 0.4 2010-04-01 14745.9 1.0 2010-07-01 14845.5 0.7 2010-10-01 14939.0 0.6 2011-01-01 14881.3 -0.4 2011-04-01 14989.6 0.7 2011-07-01 15021.1 0.2 2011-10-01 15190.3 1.1 2012-01-01 15291.0 0.7 2012-04-01 15362.4 0.5 2012-07-01 15380.8 0.1 2012-10-01 15384.3 0.0 2013-01-01 15491.9 0.7 2013-04-01 15521.6 0.2 2013-07-01 15641.3 0.8 2013-10-01 15793.9 1.0 2014-01-01 15757.6 -0.2 2014-04-01 15935.8 1.1 2014-07-01 16139.5 1.3 2014-10-01 16220.2 0.5 2015-01-01 16350.0 0.8 2015-04-01 16460.9 0.7 2015-07-01 16527.6 0.4 2015-10-01 16547.6 0.1 2016-01-01 16571.6 0.2 2016-04-01 16663.5 0.6 2016-07-01 16778.1 0.7 2016-10-01 16851.4 0.4 2017-01-01 16903.2 0.3 2017-04-01 17030.0 0.8

Explanation / Answer

Null Hypothesis : H0 : Level of real GDP is stationary. % Average Quarterly GDP change = 0

Alternative Hypothesis : Ha : Level of real GDP is not stationary. % Average Quarterly GDP change 0

Mean Quarterly Average GDP change xbar = 0.7854 %

Standard Deviation of Average Quartly GDP change s = 0.9498 %

number of quarters = 281 quarters

Test Statistic

Z = xbar/(s/sqrt(n))

Z = 0.7894/ (0.9498/sqrt(281))

Z = 0.7894/ 0.05666

Z = 13.93

so for 95% confidence interval, Zcritical = 1.96

so, here Z > Zcritical , here we can reject the null hypothesis and can conclude that Level of real GDP is not stationary.

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