Question

observation_date	FEDFUNDS
1954-07-01	0.80
1954-08-01	1.22
1954-09-01	1.06
1954-10-01	0.85
1954-11-01	0.83
1954-12-01	1.28
1955-01-01	1.39
1955-02-01	1.29
1955-03-01	1.35
1955-04-01	1.43
1955-05-01	1.43
1955-06-01	1.64
1955-07-01	1.68
1955-08-01	1.96
1955-09-01	2.18
1955-10-01	2.24
1955-11-01	2.35
1955-12-01	2.48
1956-01-01	2.45
1956-02-01	2.50
1956-03-01	2.50
1956-04-01	2.62
1956-05-01	2.75
1956-06-01	2.71
1956-07-01	2.75
1956-08-01	2.73
1956-09-01	2.95
1956-10-01	2.96
1956-11-01	2.88
1956-12-01	2.94
1957-01-01	2.84
1957-02-01	3.00
1957-03-01	2.96
1957-04-01	3.00
1957-05-01	3.00
1957-06-01	3.00
1957-07-01	2.99
1957-08-01	3.24
1957-09-01	3.47
1957-10-01	3.50
1957-11-01	3.28
1957-12-01	2.98
1958-01-01	2.72
1958-02-01	1.67
1958-03-01	1.20
1958-04-01	1.26
1958-05-01	0.63
1958-06-01	0.93
1958-07-01	0.68
1958-08-01	1.53
1958-09-01	1.76
1958-10-01	1.80
1958-11-01	2.27
1958-12-01	2.42
1959-01-01	2.48
1959-02-01	2.43
1959-03-01	2.80
1959-04-01	2.96
1959-05-01	2.90
1959-06-01	3.39
1959-07-01	3.47
1959-08-01	3.50
1959-09-01	3.76
1959-10-01	3.98
1959-11-01	4.00
1959-12-01	3.99
1960-01-01	3.99
1960-02-01	3.97
1960-03-01	3.84
1960-04-01	3.92
1960-05-01	3.85
1960-06-01	3.32
1960-07-01	3.23
1960-08-01	2.98
1960-09-01	2.60
1960-10-01	2.47
1960-11-01	2.44
1960-12-01	1.98
1961-01-01	1.45
1961-02-01	2.54
1961-03-01	2.02
1961-04-01	1.49
1961-05-01	1.98
1961-06-01	1.73
1961-07-01	1.17
1961-08-01	2.00
1961-09-01	1.88
1961-10-01	2.26
1961-11-01	2.61
1961-12-01	2.33
1962-01-01	2.15
1962-02-01	2.37
1962-03-01	2.85
1962-04-01	2.78
1962-05-01	2.36
1962-06-01	2.68
1962-07-01	2.71
1962-08-01	2.93
1962-09-01	2.90
1962-10-01	2.90
1962-11-01	2.94
1962-12-01	2.93
1963-01-01	2.92
1963-02-01	3.00
1963-03-01	2.98
1963-04-01	2.90
1963-05-01	3.00
1963-06-01	2.99
1963-07-01	3.02
1963-08-01	3.49
1963-09-01	3.48
1963-10-01	3.50
1963-11-01	3.48
1963-12-01	3.38
1964-01-01	3.48
1964-02-01	3.48
1964-03-01	3.43
1964-04-01	3.47
1964-05-01	3.50
1964-06-01	3.50
1964-07-01	3.42
1964-08-01	3.50
1964-09-01	3.45
1964-10-01	3.36
1964-11-01	3.52
1964-12-01	3.85
1965-01-01	3.90
1965-02-01	3.98
1965-03-01	4.04
1965-04-01	4.09
1965-05-01	4.10
1965-06-01	4.04
1965-07-01	4.09
1965-08-01	4.12
1965-09-01	4.01
1965-10-01	4.08
1965-11-01	4.10
1965-12-01	4.32
1966-01-01	4.42
1966-02-01	4.60
1966-03-01	4.65
1966-04-01	4.67
1966-05-01	4.90
1966-06-01	5.17
1966-07-01	5.30
1966-08-01	5.53
1966-09-01	5.40
1966-10-01	5.53
1966-11-01	5.76
1966-12-01	5.40
1967-01-01	4.94
1967-02-01	5.00
1967-03-01	4.53
1967-04-01	4.05
1967-05-01	3.94
1967-06-01	3.98
1967-07-01	3.79
1967-08-01	3.90
1967-09-01	3.99
1967-10-01	3.88
1967-11-01	4.13
1967-12-01	4.51
1968-01-01	4.60
1968-02-01	4.71
1968-03-01	5.05
1968-04-01	5.76
1968-05-01	6.11
1968-06-01	6.07
1968-07-01	6.02
1968-08-01	6.03
1968-09-01	5.78
1968-10-01	5.91
1968-11-01	5.82
1968-12-01	6.02
1969-01-01	6.30
1969-02-01	6.61
1969-03-01	6.79
1969-04-01	7.41
1969-05-01	8.67
1969-06-01	8.90
1969-07-01	8.61
1969-08-01	9.19
1969-09-01	9.15
1969-10-01	9.00
1969-11-01	8.85
1969-12-01	8.97
1970-01-01	8.98
1970-02-01	8.98
1970-03-01	7.76
1970-04-01	8.10
1970-05-01	7.94
1970-06-01	7.60
1970-07-01	7.21
1970-08-01	6.61
1970-09-01	6.29
1970-10-01	6.20
1970-11-01	5.60
1970-12-01	4.90
1971-01-01	4.14
1971-02-01	3.72
1971-03-01	3.71
1971-04-01	4.15
1971-05-01	4.63
1971-06-01	4.91
1971-07-01	5.31
1971-08-01	5.56
1971-09-01	5.55
1971-10-01	5.20
1971-11-01	4.91
1971-12-01	4.14
1972-01-01	3.50
1972-02-01	3.29
1972-03-01	3.83
1972-04-01	4.17
1972-05-01	4.27
1972-06-01	4.46
1972-07-01	4.55
1972-08-01	4.80
1972-09-01	4.87
1972-10-01	5.04
1972-11-01	5.06
1972-12-01	5.33
1973-01-01	5.94
1973-02-01	6.58
1973-03-01	7.09
1973-04-01	7.12
1973-05-01	7.84
1973-06-01	8.49
1973-07-01	10.40
1973-08-01	10.50
1973-09-01	10.78
1973-10-01	10.01
1973-11-01	10.03
1973-12-01	9.95
1974-01-01	9.65
1974-02-01	8.97
1974-03-01	9.35
1974-04-01	10.51
1974-05-01	11.31
1974-06-01	11.93
1974-07-01	12.92
1974-08-01	12.01
1974-09-01	11.34
1974-10-01	10.06
1974-11-01	9.45
1974-12-01	8.53
1975-01-01	7.13
1975-02-01	6.24
1975-03-01	5.54
1975-04-01	5.49
1975-05-01	5.22
1975-06-01	5.55
1975-07-01	6.10
1975-08-01	6.14
1975-09-01	6.24
1975-10-01	5.82
1975-11-01	5.22
1975-12-01	5.20
1976-01-01	4.87
1976-02-01	4.77
1976-03-01	4.84
1976-04-01	4.82
1976-05-01	5.29
1976-06-01	5.48
1976-07-01	5.31
1976-08-01	5.29
1976-09-01	5.25
1976-10-01	5.02
1976-11-01	4.95
1976-12-01	4.65
1977-01-01	4.61
1977-02-01	4.68
1977-03-01	4.69
1977-04-01	4.73
1977-05-01	5.35
1977-06-01	5.39
1977-07-01	5.42
1977-08-01	5.90
1977-09-01	6.14
1977-10-01	6.47
1977-11-01	6.51
1977-12-01	6.56
1978-01-01	6.70
1978-02-01	6.78
1978-03-01	6.79
1978-04-01	6.89
1978-05-01	7.36
1978-06-01	7.60
1978-07-01	7.81
1978-08-01	8.04
1978-09-01	8.45
1978-10-01	8.96
1978-11-01	9.76
1978-12-01	10.03
1979-01-01	10.07
1979-02-01	10.06
1979-03-01	10.09
1979-04-01	10.01
1979-05-01	10.24
1979-06-01	10.29
1979-07-01	10.47
1979-08-01	10.94
1979-09-01	11.43
1979-10-01	13.77
1979-11-01	13.18
1979-12-01	13.78
1980-01-01	13.82
1980-02-01	14.13
1980-03-01	17.19
1980-04-01	17.61
1980-05-01	10.98
1980-06-01	9.47
1980-07-01	9.03
1980-08-01	9.61
1980-09-01	10.87
1980-10-01	12.81
1980-11-01	15.85
1980-12-01	18.90
1981-01-01	19.08
1981-02-01	15.93
1981-03-01	14.70
1981-04-01	15.72
1981-05-01	18.52
1981-06-01	19.10
1981-07-01	19.04
1981-08-01	17.82
1981-09-01	15.87
1981-10-01	15.08
1981-11-01	13.31
1981-12-01	12.37
1982-01-01	13.22
1982-02-01	14.78
1982-03-01	14.68
1982-04-01	14.94
1982-05-01	14.45
1982-06-01	14.15
1982-07-01	12.59
1982-08-01	10.12
1982-09-01	10.31
1982-10-01	9.71
1982-11-01	9.20
1982-12-01	8.95
1983-01-01	8.68
1983-02-01	8.51
1983-03-01	8.77
1983-04-01	8.80
1983-05-01	8.63
1983-06-01	8.98
1983-07-01	9.37
1983-08-01	9.56
1983-09-01	9.45
1983-10-01	9.48
1983-11-01	9.34
1983-12-01	9.47
1984-01-01	9.56
1984-02-01	9.59
1984-03-01	9.91
1984-04-01	10.29
1984-05-01	10.32
1984-06-01	11.06
1984-07-01	11.23
1984-08-01	11.64
1984-09-01	11.30
1984-10-01	9.99
1984-11-01	9.43
1984-12-01	8.38
1985-01-01	8.35
1985-02-01	8.50
1985-03-01	8.58
1985-04-01	8.27
1985-05-01	7.97
1985-06-01	7.53
1985-07-01	7.88
1985-08-01	7.90
1985-09-01	7.92
1985-10-01	7.99
1985-11-01	8.05
1985-12-01	8.27
1986-01-01	8.14
1986-02-01	7.86
1986-03-01	7.48
1986-04-01	6.99
1986-05-01	6.85
1986-06-01	6.92
1986-07-01	6.56
1986-08-01	6.17
1986-09-01	5.89
1986-10-01	5.85
1986-11-01	6.04
1986-12-01	6.91
1987-01-01	6.43
1987-02-01	6.10
1987-03-01	6.13
1987-04-01	6.37
1987-05-01	6.85
1987-06-01	6.73
1987-07-01	6.58
1987-08-01	6.73
1987-09-01	7.22
1987-10-01	7.29
1987-11-01	6.69
1987-12-01	6.77
1988-01-01	6.83
1988-02-01	6.58
1988-03-01	6.58
1988-04-01	6.87
1988-05-01	7.09
1988-06-01	7.51
1988-07-01	7.75
1988-08-01	8.01
1988-09-01	8.19
1988-10-01	8.30
1988-11-01	8.35
1988-12-01	8.76
1989-01-01	9.12
1989-02-01	9.36
1989-03-01	9.85
1989-04-01	9.84
1989-05-01	9.81
1989-06-01	9.53
1989-07-01	9.24
1989-08-01	8.99
1989-09-01	9.02
1989-10-01	8.84
1989-11-01	8.55
1989-12-01	8.45
1990-01-01	8.23
1990-02-01	8.24
1990-03-01	8.28
1990-04-01	8.26
1990-05-01	8.18
1990-06-01	8.29
1990-07-01	8.15
1990-08-01	8.13
1990-09-01	8.20
1990-10-01	8.11
1990-11-01	7.81
1990-12-01	7.31
1991-01-01	6.91
1991-02-01	6.25
1991-03-01	6.12
1991-04-01	5.91
1991-05-01	5.78
1991-06-01	5.90
1991-07-01	5.82
1991-08-01	5.66
1991-09-01	5.45
1991-10-01	5.21
1991-11-01	4.81
1991-12-01	4.43
1992-01-01	4.03
1992-02-01	4.06
1992-03-01	3.98
1992-04-01	3.73
1992-05-01	3.82
1992-06-01	3.76
1992-07-01	3.25
1992-08-01	3.30
1992-09-01	3.22
1992-10-01	3.10
1992-11-01	3.09
1992-12-01	2.92
1993-01-01	3.02
1993-02-01	3.03
1993-03-01	3.07
1993-04-01	2.96
1993-05-01	3.00
1993-06-01	3.04
1993-07-01	3.06
1993-08-01	3.03
1993-09-01	3.09
1993-10-01	2.99
1993-11-01	3.02
1993-12-01	2.96
1994-01-01	3.05
1994-02-01	3.25
1994-03-01	3.34
1994-04-01	3.56
1994-05-01	4.01
1994-06-01	4.25
1994-07-01	4.26
1994-08-01	4.47
1994-09-01	4.73
1994-10-01	4.76
1994-11-01	5.29
1994-12-01	5.45
1995-01-01	5.53
1995-02-01	5.92
1995-03-01	5.98
1995-04-01	6.05
1995-05-01	6.01
1995-06-01	6.00
1995-07-01	5.85
1995-08-01	5.74
1995-09-01	5.80
1995-10-01	5.76
1995-11-01	5.80
1995-12-01	5.60
1996-01-01	5.56
1996-02-01	5.22
1996-03-01	5.31
1996-04-01	5.22
1996-05-01	5.24
1996-06-01	5.27
1996-07-01	5.40
1996-08-01	5.22
1996-09-01	5.30
1996-10-01	5.24
1996-11-01	5.31
1996-12-01	5.29
1997-01-01	5.25
1997-02-01	5.19
1997-03-01	5.39
1997-04-01	5.51
1997-05-01	5.50
1997-06-01	5.56
1997-07-01	5.52
1997-08-01	5.54
1997-09-01	5.54
1997-10-01	5.50
1997-11-01	5.52
1997-12-01	5.50
1998-01-01	5.56
1998-02-01	5.51
1998-03-01	5.49
1998-04-01	5.45
1998-05-01	5.49
1998-06-01	5.56
1998-07-01	5.54
1998-08-01	5.55
1998-09-01	5.51
1998-10-01	5.07
1998-11-01	4.83
1998-12-01	4.68
1999-01-01	4.63
1999-02-01	4.76
1999-03-01	4.81
1999-04-01	4.74
1999-05-01	4.74
1999-06-01	4.76
1999-07-01	4.99
1999-08-01	5.07
1999-09-01	5.22
1999-10-01	5.20
1999-11-01	5.42
1999-12-01	5.30
2000-01-01	5.45
2000-02-01	5.73
2000-03-01	5.85
2000-04-01	6.02
2000-05-01	6.27
2000-06-01	6.53
2000-07-01	6.54
2000-08-01	6.50
2000-09-01	6.52
2000-10-01	6.51
2000-11-01	6.51
2000-12-01	6.40
2001-01-01	5.98
2001-02-01	5.49
2001-03-01	5.31
2001-04-01	4.80
2001-05-01	4.21
2001-06-01	3.97
2001-07-01	3.77
2001-08-01	3.65
2001-09-01	3.07
2001-10-01	2.49
2001-11-01	2.09
2001-12-01	1.82
2002-01-01	1.73
2002-02-01	1.74
2002-03-01	1.73
2002-04-01	1.75
2002-05-01	1.75
2002-06-01	1.75
2002-07-01	1.73
2002-08-01	1.74
2002-09-01	1.75
2002-10-01	1.75
2002-11-01	1.34
2002-12-01	1.24
2003-01-01	1.24
2003-02-01	1.26
2003-03-01	1.25
2003-04-01	1.26
2003-05-01	1.26
2003-06-01	1.22
2003-07-01	1.01
2003-08-01	1.03
2003-09-01	1.01
2003-10-01	1.01
2003-11-01	1.00
2003-12-01	0.98
2004-01-01	1.00
2004-02-01	1.01
2004-03-01	1.00
2004-04-01	1.00
2004-05-01	1.00
2004-06-01	1.03
2004-07-01	1.26
2004-08-01	1.43
2004-09-01	1.61
2004-10-01	1.76
2004-11-01	1.93
2004-12-01	2.16
2005-01-01	2.28
2005-02-01	2.50
2005-03-01	2.63
2005-04-01	2.79
2005-05-01	3.00
2005-06-01	3.04
2005-07-01	3.26
2005-08-01	3.50
2005-09-01	3.62
2005-10-01	3.78
2005-11-01	4.00
2005-12-01	4.16
2006-01-01	4.29
2006-02-01	4.49
2006-03-01	4.59
2006-04-01	4.79
2006-05-01	4.94
2006-06-01	4.99
2006-07-01	5.24
2006-08-01	5.25
2006-09-01	5.25
2006-10-01	5.25
2006-11-01	5.25
2006-12-01	5.24
2007-01-01	5.25
2007-02-01	5.26
2007-03-01	5.26
2007-04-01	5.25
2007-05-01	5.25
2007-06-01	5.25
2007-07-01	5.26
2007-08-01	5.02
2007-09-01	4.94
2007-10-01	4.76
2007-11-01	4.49
2007-12-01	4.24
2008-01-01	3.94
2008-02-01	2.98
2008-03-01	2.61
2008-04-01	2.28
2008-05-01	1.98
2008-06-01	2.00
2008-07-01	2.01
2008-08-01	2.00
2008-09-01	1.81
2008-10-01	0.97
2008-11-01	0.39
2008-12-01	0.16
2009-01-01	0.15
2009-02-01	0.22
2009-03-01	0.18
2009-04-01	0.15
2009-05-01	0.18
2009-06-01	0.21
2009-07-01	0.16
2009-08-01	0.16
2009-09-01	0.15
2009-10-01	0.12
2009-11-01	0.12
2009-12-01	0.12
2010-01-01	0.11
2010-02-01	0.13
2010-03-01	0.16
2010-04-01	0.20
2010-05-01	0.20
2010-06-01	0.18
2010-07-01	0.18
2010-08-01	0.19
2010-09-01	0.19
2010-10-01	0.19
2010-11-01	0.19
2010-12-01	0.18
2011-01-01	0.17
2011-02-01	0.16
2011-03-01	0.14
2011-04-01	0.10
2011-05-01	0.09
2011-06-01	0.09
2011-07-01	0.07
2011-08-01	0.10
2011-09-01	0.08
2011-10-01	0.07
2011-11-01	0.08
2011-12-01	0.07
2012-01-01	0.08
2012-02-01	0.10
2012-03-01	0.13
2012-04-01	0.14
2012-05-01	0.16
2012-06-01	0.16
2012-07-01	0.16
2012-08-01	0.13
2012-09-01	0.14
2012-10-01	0.16
2012-11-01	0.16
2012-12-01	0.16
2013-01-01	0.14
2013-02-01	0.15
2013-03-01	0.14
2013-04-01	0.15
2013-05-01	0.11
2013-06-01	0.09
2013-07-01	0.09
2013-08-01	0.08
2013-09-01	0.08
2013-10-01	0.09
2013-11-01	0.08
2013-12-01	0.09
2014-01-01	0.07
2014-02-01	0.07
2014-03-01	0.08
2014-04-01	0.09
2014-05-01	0.09
2014-06-01	0.10
2014-07-01	0.09
2014-08-01	0.09
2014-09-01	0.09
2014-10-01	0.09
2014-11-01	0.09
2014-12-01	0.12
2015-01-01	0.11
2015-02-01	0.11
2015-03-01	0.11
2015-04-01	0.12
2015-05-01	0.12

Using the data in the Federal Funds Rate tab in the data file, perform the following analysese.

a) Create a new column in the data file with the 5 period moving average series of the Federal Funds rate.

b) Create a new column in the data file with the expontential smoothing series with W=0.25.

c) Plot the three columns against the date.

d) Fit an Autoregressive model to this data, assume that the true model has only one lag in it.

Answer 1

observation_date	FEDFUNDS	5 year moving averagestotals	smoothened values
01-07-1954	0.8
01-08-1954	1.22
01-09-1954	1.06	1.006666667	#N/A
01-10-1954	0.85	1.048	1.006666667
01-11-1954	0.83	1.082	1.037666667
01-12-1954	1.28	1.128	1.070916667
01-01-1955	1.39	1.228	1.113729167
01-02-1955	1.29	1.348	1.199432292
01-03-1955	1.35	1.378	1.310858073
01-04-1955	1.43	1.428	1.361214518
01-05-1955	1.43	1.506	1.41130363
01-06-1955	1.64	1.628	1.482325907
01-07-1955	1.68	1.778	1.591581477
01-08-1955	1.96	1.94	1.731395369
01-09-1955	2.18	2.082	1.887848842
01-10-1955	2.24	2.242	2.033462211
01-11-1955	2.35	2.34	2.189865553
01-12-1955	2.48	2.404	2.302466388
01-01-1956	2.45	2.456	2.378616597

i have given few values since i wasnt permitted to answer more than 65000 woeds

i have used excel to do these calculations

i have entered the given data in excel with observation date in column A and FEDFUNDS in column B

=AVERAGE(B2:B6) i have used this formula in the cell C4

in C5 i have used =AVERAGE(B3:B7)

likewise by using drag option in the excel i have found the values till C730

for smoothened values i have installed the add in analysis toolpak

on the menu bar i opened data and then data analysis

i have choosen eponential smoothing and clickd ok

filled the details as in the picture below

the smoothened values will displayed

now select whole data and go to insert and then click scatter plot

our auto regressive model is y_t = a + b y_t-1 + error

so now copy the fedfunds value in E column and copy the values in E2 to E732 in F3 to F733

now open data analysis and click regression and fill the details as shown in the given picture

click ok and the result is displayed in new sheet

so from the results our model is

y_t = 0.050097 +  y_t-1