Homework 3
Omar Alenezy
February 24, 2016
Question1: From Category A, I will choose Real Gross Private Domestic Investment
From Category B, I will choose NYSE Composite Index
From Category C, I will choose 10-year Treasury Constant Maturity Rate
library("Quandl")## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric#Real Gross Private Investment
pi<- Quandl("FRED/GPDIC1", type="ts")
str(pi)## Time-Series [1:276] from 1947 to 2016: 223 206 200 238 263 ...zooreg(1:276, start=c(1947,1), frequency=4)## 1947(1) 1947(2) 1947(3) 1947(4) 1948(1) 1948(2) 1948(3) 1948(4) 1949(1)
## 1 2 3 4 5 6 7 8 9
## 1949(2) 1949(3) 1949(4) 1950(1) 1950(2) 1950(3) 1950(4) 1951(1) 1951(2)
## 10 11 12 13 14 15 16 17 18
## 1951(3) 1951(4) 1952(1) 1952(2) 1952(3) 1952(4) 1953(1) 1953(2) 1953(3)
## 19 20 21 22 23 24 25 26 27
## 1953(4) 1954(1) 1954(2) 1954(3) 1954(4) 1955(1) 1955(2) 1955(3) 1955(4)
## 28 29 30 31 32 33 34 35 36
## 1956(1) 1956(2) 1956(3) 1956(4) 1957(1) 1957(2) 1957(3) 1957(4) 1958(1)
## 37 38 39 40 41 42 43 44 45
## 1958(2) 1958(3) 1958(4) 1959(1) 1959(2) 1959(3) 1959(4) 1960(1) 1960(2)
## 46 47 48 49 50 51 52 53 54
## 1960(3) 1960(4) 1961(1) 1961(2) 1961(3) 1961(4) 1962(1) 1962(2) 1962(3)
## 55 56 57 58 59 60 61 62 63
## 1962(4) 1963(1) 1963(2) 1963(3) 1963(4) 1964(1) 1964(2) 1964(3) 1964(4)
## 64 65 66 67 68 69 70 71 72
## 1965(1) 1965(2) 1965(3) 1965(4) 1966(1) 1966(2) 1966(3) 1966(4) 1967(1)
## 73 74 75 76 77 78 79 80 81
## 1967(2) 1967(3) 1967(4) 1968(1) 1968(2) 1968(3) 1968(4) 1969(1) 1969(2)
## 82 83 84 85 86 87 88 89 90
## 1969(3) 1969(4) 1970(1) 1970(2) 1970(3) 1970(4) 1971(1) 1971(2) 1971(3)
## 91 92 93 94 95 96 97 98 99
## 1971(4) 1972(1) 1972(2) 1972(3) 1972(4) 1973(1) 1973(2) 1973(3) 1973(4)
## 100 101 102 103 104 105 106 107 108
## 1974(1) 1974(2) 1974(3) 1974(4) 1975(1) 1975(2) 1975(3) 1975(4) 1976(1)
## 109 110 111 112 113 114 115 116 117
## 1976(2) 1976(3) 1976(4) 1977(1) 1977(2) 1977(3) 1977(4) 1978(1) 1978(2)
## 118 119 120 121 122 123 124 125 126
## 1978(3) 1978(4) 1979(1) 1979(2) 1979(3) 1979(4) 1980(1) 1980(2) 1980(3)
## 127 128 129 130 131 132 133 134 135
## 1980(4) 1981(1) 1981(2) 1981(3) 1981(4) 1982(1) 1982(2) 1982(3) 1982(4)
## 136 137 138 139 140 141 142 143 144
## 1983(1) 1983(2) 1983(3) 1983(4) 1984(1) 1984(2) 1984(3) 1984(4) 1985(1)
## 145 146 147 148 149 150 151 152 153
## 1985(2) 1985(3) 1985(4) 1986(1) 1986(2) 1986(3) 1986(4) 1987(1) 1987(2)
## 154 155 156 157 158 159 160 161 162
## 1987(3) 1987(4) 1988(1) 1988(2) 1988(3) 1988(4) 1989(1) 1989(2) 1989(3)
## 163 164 165 166 167 168 169 170 171
## 1989(4) 1990(1) 1990(2) 1990(3) 1990(4) 1991(1) 1991(2) 1991(3) 1991(4)
## 172 173 174 175 176 177 178 179 180
## 1992(1) 1992(2) 1992(3) 1992(4) 1993(1) 1993(2) 1993(3) 1993(4) 1994(1)
## 181 182 183 184 185 186 187 188 189
## 1994(2) 1994(3) 1994(4) 1995(1) 1995(2) 1995(3) 1995(4) 1996(1) 1996(2)
## 190 191 192 193 194 195 196 197 198
## 1996(3) 1996(4) 1997(1) 1997(2) 1997(3) 1997(4) 1998(1) 1998(2) 1998(3)
## 199 200 201 202 203 204 205 206 207
## 1998(4) 1999(1) 1999(2) 1999(3) 1999(4) 2000(1) 2000(2) 2000(3) 2000(4)
## 208 209 210 211 212 213 214 215 216
## 2001(1) 2001(2) 2001(3) 2001(4) 2002(1) 2002(2) 2002(3) 2002(4) 2003(1)
## 217 218 219 220 221 222 223 224 225
## 2003(2) 2003(3) 2003(4) 2004(1) 2004(2) 2004(3) 2004(4) 2005(1) 2005(2)
## 226 227 228 229 230 231 232 233 234
## 2005(3) 2005(4) 2006(1) 2006(2) 2006(3) 2006(4) 2007(1) 2007(2) 2007(3)
## 235 236 237 238 239 240 241 242 243
## 2007(4) 2008(1) 2008(2) 2008(3) 2008(4) 2009(1) 2009(2) 2009(3) 2009(4)
## 244 245 246 247 248 249 250 251 252
## 2010(1) 2010(2) 2010(3) 2010(4) 2011(1) 2011(2) 2011(3) 2011(4) 2012(1)
## 253 254 255 256 257 258 259 260 261
## 2012(2) 2012(3) 2012(4) 2013(1) 2013(2) 2013(3) 2013(4) 2014(1) 2014(2)
## 262 263 264 265 266 267 268 269 270
## 2014(3) 2014(4) 2015(1) 2015(2) 2015(3) 2015(4)
## 271 272 273 274 275 276image: 
lnpi <- log(pi)
par(mfrow=c(2,2))
plot(pi, xlab = "period", ylab = "Private Investment", main= "Real Gross Private Investment")
plot(lnpi, xlab = "Period", ylab = "log(Investment)")
plot(diff(pi))
plot(diff(lnpi))
library(tseries)
adf.test(pi)##
## Augmented Dickey-Fuller Test
##
## data: pi
## Dickey-Fuller = -2.7222, Lag order = 6, p-value = 0.2718
## alternative hypothesis: stationaryadf.test(lnpi) ##
## Augmented Dickey-Fuller Test
##
## data: lnpi
## Dickey-Fuller = -2.6039, Lag order = 6, p-value = 0.3216
## alternative hypothesis: stationaryadf.test(diff(pi))## Warning in adf.test(diff(pi)): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff(pi)
## Dickey-Fuller = -5.3713, Lag order = 6, p-value = 0.01
## alternative hypothesis: stationaryadf.test(diff(lnpi))## Warning in adf.test(diff(lnpi)): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff(lnpi)
## Dickey-Fuller = -7.3938, Lag order = 6, p-value = 0.01
## alternative hypothesis: stationarykpss.test(pi,null ="Trend")## Warning in kpss.test(pi, null = "Trend"): p-value smaller than printed p-
## value##
## KPSS Test for Trend Stationarity
##
## data: pi
## KPSS Trend = 1.0029, Truncation lag parameter = 3, p-value = 0.01kpss.test(lnpi, null = "Trend")## Warning in kpss.test(lnpi, null = "Trend"): p-value smaller than printed p-
## value##
## KPSS Test for Trend Stationarity
##
## data: lnpi
## KPSS Trend = 0.44857, Truncation lag parameter = 3, p-value = 0.01kpss.test(diff(pi), null = "Level")## Warning in kpss.test(diff(pi), null = "Level"): p-value greater than
## printed p-value##
## KPSS Test for Level Stationarity
##
## data: diff(pi)
## KPSS Level = 0.17082, Truncation lag parameter = 3, p-value = 0.1kpss.test(diff(lnpi), null="Level")## Warning in kpss.test(diff(lnpi), null = "Level"): p-value greater than
## printed p-value##
## KPSS Test for Level Stationarity
##
## data: diff(lnpi)
## KPSS Level = 0.03644, Truncation lag parameter = 3, p-value = 0.1Category B: NYSE
library("Quandl")ny <- Quandl("YAHOO/INDEX_NY")
tail(ny)## Date Open High Low Close Volume Adjusted Close
## 3044 2004-01-20 5708.74 5725.34 5693.47 5701.47 1700 5701.47
## 3045 2004-01-16 5683.17 5708.89 5680.70 5707.60 0 5707.60
## 3046 2004-01-15 5667.44 5704.04 5643.79 5681.52 0 5681.52
## 3047 2004-01-14 5622.37 5667.89 5622.37 5667.55 0 5667.55
## 3048 2004-01-13 5653.33 5661.72 5593.27 5622.37 0 5622.37
## 3049 2004-01-12 5630.43 5655.28 5627.70 5653.31 1700 5653.31ny <- rev(ny[,7])
tny<-ts(ny)
head(ny)## [1] 5653.31 5622.37 5667.55 5681.52 5707.60 5701.47str(tny)## Time-Series [1:3049] from 1 to 3049: 5653 5622 5668 5682 5708 ...par(mfrow= c(1,2))
plot(tny, xlab = "Period", ylab ="Closing Price", main= "NYSE Composite Index")
plot(diff(tny))
adf.test(tny)##
## Augmented Dickey-Fuller Test
##
## data: tny
## Dickey-Fuller = -1.4514, Lag order = 14, p-value = 0.8106
## alternative hypothesis: stationaryadf.test(diff(tny))## Warning in adf.test(diff(tny)): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff(tny)
## Dickey-Fuller = -15.6, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationarykpss.test(tny, null= "Trend")## Warning in kpss.test(tny, null = "Trend"): p-value smaller than printed p-
## value##
## KPSS Test for Trend Stationarity
##
## data: tny
## KPSS Trend = 3.8366, Truncation lag parameter = 12, p-value = 0.01kpss.test(diff(tny), null="Level")## Warning in kpss.test(diff(tny), null = "Level"): p-value greater than
## printed p-value##
## KPSS Test for Level Stationarity
##
## data: diff(tny)
## KPSS Level = 0.12761, Truncation lag parameter = 12, p-value = 0.1Category C: 10-Year Treasury Constant Maturity
tm <- Quandl("FRED/DGS10", type="zoo")
head(tm)## 1962-01-02 1962-01-03 1962-01-04 1962-01-05 1962-01-08 1962-01-09
## 4.06 4.03 3.99 4.02 4.03 4.05par(mfrow=c(1,2))
plot(tm,xlab=" Period", ylab = "Treasury Rate")
plot(diff(tm))
adf.test(tm)##
## Augmented Dickey-Fuller Test
##
## data: tm
## Dickey-Fuller = -2.0945, Lag order = 23, p-value = 0.5384
## alternative hypothesis: stationarykpss.test(tm, null="Trend")## Warning in kpss.test(tm, null = "Trend"): p-value smaller than printed p-
## value##
## KPSS Test for Trend Stationarity
##
## data: tm
## KPSS Trend = 9.2783, Truncation lag parameter = 26, p-value = 0.01kpss.test(diff(tm), null="Level")## Warning in kpss.test(diff(tm), null = "Level"): p-value greater than
## printed p-value##
## KPSS Test for Level Stationarity
##
## data: diff(tm)
## KPSS Level = 0.23875, Truncation lag parameter = 26, p-value = 0.1