Time Series

(1) Consider the growth rates of the U.S. quarterly gross national product (GNP) from 1947.I to 2011.IV. The original data, from the Federal Reserve Bank of St Louis, are in the file q-gnp-4711.txt (year, month, day, gnp), and the GNP is in billions of dollars. The growth rate is the first differenced series of the log(GNP).

(a) Plot the GNP growth rates. The reduction in volatility, starting in the 1980s, is referred 

to as the great moderation in the economic literature.

(b) Build an AR(3) model for the growth rate series. 

(c) Does the model confirm the existence of business cycles? Explain.

(d) Is the model you fitted a causal AR process?

 

(2) Consider the data in the file Strikes.txt. 

(a) Difference the data twice at lag 1 and subtract the mean.

(b) Fit an AR(2) model for the strikes data.

(c) Is the model you fitted a causal AR process?

(d) Find the values of the model autocorrelation function rho(k) for k >=0 for the fitted model.

(e) Plot the sample and model autocorrelation functions.

 

See attachement for data. This hwk is due on Sunday at 10 pm. 

4737
5117
5091
3468
4320
3825
3673
3694
3708
3333
3367
3614
3362
3655
3963
4405
4595
5045
5700
5716
5138
5010
5353
6074
5031
5648
5506
4230
4827
3885

year mon day gnp
1947 01 01 238.1
1947 04 01 241.5
1947 07 01 245.6
1947 10 01 255.6
1948 01 01 261.7
1948 04 01 268.7
1948 07 01 275.3
1948 10 01 276.6
1949 01 01 271.3
1949 04 01 267.5
1949 07 01 268.9
1949 10 01 266.3
1950 01 01 276.4
1950 04 01 285.8
1950 07 01 303.5
1950 10 01 314.9
1951 01 01 330.5
1951 04 01 338.5
1951 07 01 345.5
1951 10 01 350.1
1952 01 01 353.2
1952 04 01 354.2
1952 07 01 360.5
1952 10 01 373.3
1953 01 01 380.3
1953 04 01 384.0
1953 07 01 382.9
1953 10 01 377.7
1954 01 01 377.2
1954 04 01 378.0
1954 07 01 382.8
1954 10 01 391.8
1955 01 01 405.0
1955 04 01 413.3
1955 07 01 421.9
1955 10 01 428.5
1956 01 01 431.1
1956 04 01 437.0
1956 07 01 442.1
1956 10 01 450.6
1957 01 01 460.3
1957 04 01 462.5
1957 07 01 469.6
1957 10 01 464.0
1958 01 01 456.6
1958 04 01 460.7
1958 07 01 474.3
1958 10 01 487.6
1959 01 01 498.1
1959 04 01 511.1
1959 07 01 512.1
1959 10 01 516.3
1960 01 01 529.9
1960 04 01 529.2
1960 07 01 532.1
1960 10 01 527.0
1961 01 01 531.5
1961 04 01 542.4
1961 07 01 553.0
1961 10 01 566.2
1962 01 01 579.7
1962 04 01 587.2
1962 07 01 594.1
1962 10 01 598.1
1963 01 01 607.0
1963 04 01 615.5
1963 07 01 628.4
1963 10 01 638.1
1964 01 01 654.7
1964 04 01 663.7
1964 07 01 675.5
1964 10 01 680.3
1965 01 01 701.1
1965 04 01 713.8
1965 07 01 730.4
1965 10 01 752.2
1966 01 01 775.8
1966 04 01 785.0
1966 07 01 798.1
1966 10 01 812.2
1967 01 01 823.0
1967 04 01 827.4
1967 07 01 842.7
1967 10 01 858.3
1968 01 01 885.6
1968 04 01 910.1
1968 07 01 925.5
1968 10 01 942.5
1969 01 01 967.2
1969 04 01 982.3
1969 07 01 1002.3
1969 10 01 1010.5
1970 01 01 1023.4
1970 04 01 1039.7
1970 07 01 1057.1
1970 10 01 1058.7
1971 01 01 1105.5
1971 04 01 1126.7
1971 07 01 1146.3
1971 10 01 1159.1
1972 01 01 1198.3
1972 04 01 1233.7
1972 07 01 1258.2
1972 10 01 1295.6
1973 01 01 1345.8
1973 04 01 1383.1
1973 07 01 1404.6
1973 10 01 1446.1
1974 01 01 1463.6
1974 04 01 1501.2
1974 07 01 1528.9
1974 10 01 1566.1
1975 01 01 1580.8
1975 04 01 1616.6
1975 07 01 1675.4
1975 10 01 1729.9
1976 01 01 1787.7
1976 04 01 1820.9
1976 07 01 1854.8
1976 10 01 1902.4
1977 01 01 1959.3
1977 04 01 2026.0
1977 07 01 2086.9
1977 10 01 2129.6
1978 01 01 2171.2
1978 04 01 2293.5
1978 07 01 2356.1
1978 10 01 2440.6
1979 01 01 2489.0
1979 04 01 2555.9
1979 07 01 2635.8
1979 10 01 2695.9
1980 01 01 2762.1
1980 04 01 2763.8
1980 07 01 2819.6
1980 10 01 2943.8
1981 01 01 3082.8
1981 04 01 3114.3
1981 07 01 3209.7
1981 10 01 3232.3
1982 01 01 3220.9
1982 04 01 3281.9
1982 07 01 3309.4
1982 10 01 3346.6
1983 01 01 3415.0
1983 04 01 3519.0
1983 07 01 3625.0
1983 10 01 3727.8
1984 01 01 3844.4
1984 04 01 3943.8
1984 07 01 4013.3
1984 10 01 4067.2
1985 01 01 4143.5
1985 04 01 4204.3
1985 07 01 4282.5
1985 10 01 4345.8
1986 01 01 4406.0
1986 04 01 4439.7
1986 07 01 4509.8
1986 10 01 4555.3
1987 01 01 4625.2
1987 04 01 4705.2
1987 07 01 4782.5
1987 10 01 4903.1
1988 01 01 4974.0
1988 04 01 5082.6
1988 07 01 5163.9
1988 10 01 5274.7
1989 01 01 5383.9
1989 04 01 5476.6
1989 07 01 5558.4
1989 10 01 5613.4
1990 01 01 5738.3
1990 04 01 5828.5
1990 07 01 5877.2
1990 10 01 5895.8
1991 01 01 5918.1
1991 04 01 5988.9
1991 07 01 6057.2
1991 10 01 6123.8
1992 01 01 6221.4
1992 04 01 6325.5
1992 07 01 6416.8
1992 10 01 6522.1
1993 01 01 6581.1
1993 04 01 6653.0
1993 07 01 6724.8
1993 10 01 6835.2
1994 01 01 6944.6
1994 04 01 7068.7
1994 07 01 7153.8
1994 10 01 7269.8
1995 01 01 7339.2
1995 04 01 7390.3
1995 07 01 7473.1
1995 10 01 7574.6
1996 01 01 7676.6
1996 04 01 7829.9
1996 07 01 7919.3
1996 10 01 8054.7
1997 01 01 8160.1
1997 04 01 8307.7
1997 07 01 8433.1
1997 10 01 8522.3
1998 01 01 8626.0
1998 04 01 8721.4
1998 07 01 8856.8
1998 10 01 9039.0
1999 01 01 9171.4
1999 04 01 9280.5
1999 07 01 9430.1
1999 10 01 9643.2
2000 01 01 9740.5
2000 04 01 9983.5
2000 07 01 10048.0
2000 10 01 10184.9
2001 01 01 10206.2
2001 04 01 10350.9
2001 07 01 10332.2
2001 10 01 10463.1
2002 01 01 10549.7
2002 04 01 10634.7
2002 07 01 10749.1
2002 10 01 10832.2
2003 01 01 10939.2
2003 04 01 11077.1
2003 07 01 11320.7
2003 10 01 11506.6
2004 01 01 11700.5
2004 04 01 11848.8
2004 07 01 12033.1
2004 10 01 12195.5
2005 01 01 12468.7
2005 04 01 12596.2
2005 07 01 12835.7
2005 10 01 12979.8
2006 01 01 13242.0
2006 04 01 13406.0
2006 07 01 13494.7
2006 10 01 13655.9
2007 01 01 13828.8
2007 04 01 14056.3
2007 07 01 14270.9
2007 10 01 14451.8
2008 01 01 14452.5
2008 04 01 14596.8
2008 07 01 14594.0
2008 10 01 14199.5
2009 01 01 14026.4
2009 04 01 13994.4
2009 07 01 14084.2
2009 10 01 14259.8
2010 01 01 14447.4
2010 04 01 14664.0
2010 07 01 14812.8
2010 10 01 14939.4
2011 01 01 15094.9
2011 04 01 15274.0
2011 07 01 15443.4
2011 10 01 15545.6