Time Series
Ralf Martin
spurious relations over time: the case of covid and weekly economic activity
## Warning: package 'dplyr' was built under R version 4.0.2So we got ourselves some time series data:
head(df)## week WEI Index cases deaths lnindex lockshare
## 1 2008-01-05 1.42 1.00000 0 0 0.0000000000 0
## 2 2008-01-12 1.46 1.00028 0 0 0.0002799608 0
## 3 2008-01-19 1.40 1.00055 0 0 0.0005498488 0
## 4 2008-01-26 0.96 1.00073 0 0 0.0007297337 0
## 5 2008-02-02 0.73 1.00088 0 0 0.0008796130 0
## 6 2008-02-09 0.78 1.00103 0 0 0.0010294699 0library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.0.2library(scales)
scaler=max(df$cases,na.rm=TRUE)/max(df$Index,na.rm=TRUE)
ggplot(df,aes(x=week)) + theme_minimal() + xlab("Weekly Data") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))+
scale_x_date(breaks = date_breaks("12 months"),labels = date_format("%Y")) +
geom_line(aes(y = Index*scaler, colour = "Economic Activity Index"))+
geom_line(aes(y = cases, colour = "Covid Cases per 100K"))+ylab("Covid Cases")+
scale_y_continuous(sec.axis = sec_axis(label=comma, trans=~./(scaler),
name = "Economic Activity Index"),labels=comma)
Illustration of time trend
lm(lnindex~cases,df) %>% summary()##
## Call:
## lm(formula = lnindex ~ cases, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.108375 -0.064942 -0.002043 0.055871 0.121388
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.082359 0.002731 30.156 < 2e-16 ***
## cases 0.050576 0.007800 6.484 1.74e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06928 on 669 degrees of freedom
## Multiple R-squared: 0.05913, Adjusted R-squared: 0.05772
## F-statistic: 42.04 on 1 and 669 DF, p-value: 1.736e-10df=df %>% mutate(t=1:n())
lm(lnindex~cases+t,df) %>% summary()##
## Call:
## lm(formula = lnindex ~ cases + t, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.024859 -0.004965 -0.001175 0.003861 0.038124
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.850e-02 9.170e-04 -41.98 <2e-16 ***
## cases -2.262e-02 1.393e-03 -16.23 <2e-16 ***
## t 3.752e-04 2.466e-06 152.11 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01161 on 668 degrees of freedom
## Multiple R-squared: 0.9736, Adjusted R-squared: 0.9735
## F-statistic: 1.232e+04 on 2 and 668 DF, p-value: < 2.2e-16lm(Index~cases+t,df,year(week)>2018) %>% summary()##
## Call:
## lm(formula = Index ~ cases + t, data = df, subset = year(week) >
## 2018)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0023664 -0.0006246 -0.0002099 0.0003270 0.0041289
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.674e-01 4.579e-03 211.28 <2e-16 ***
## cases -2.959e-02 2.702e-04 -109.51 <2e-16 ***
## t 4.078e-04 7.519e-06 54.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.001204 on 94 degrees of freedom
## Multiple R-squared: 0.994, Adjusted R-squared: 0.9939
## F-statistic: 7808 on 2 and 94 DF, p-value: < 2.2e-16lm(Index~cases+t+lockshare,df,year(week)>2018) %>% summary()##
## Call:
## lm(formula = Index ~ cases + t + lockshare, data = df, subset = year(week) >
## 2018)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0029987 -0.0004746 -0.0000545 0.0003908 0.0035047
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.737e-01 4.864e-03 200.179 <2e-16 ***
## cases -3.015e-02 3.169e-04 -95.129 <2e-16 ***
## t 3.971e-04 8.025e-06 49.478 <2e-16 ***
## lockshare 1.702e-05 5.604e-06 3.037 0.0031 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.001154 on 93 degrees of freedom
## Multiple R-squared: 0.9946, Adjusted R-squared: 0.9944
## F-statistic: 5664 on 3 and 93 DF, p-value: < 2.2e-16The case of Panel data
head(statsbyweek %>% arrange(state,week))## # A tibble: 6 x 9
## # Groups: state [1]
## state week hoax tweets cases deaths hoaxsh Dcases Ddeaths
## <chr> <date> <int> <int> <int> <int> <dbl> <int> <int>
## 1 Alabama 2020-03-15 4 1503 51 0 0.266 NA NA
## 2 Alabama 2020-03-22 62 4198 386 1 1.48 335 1
## 3 Alabama 2020-03-29 14 5218 1108 28 0.268 722 27
## 4 Alabama 2020-04-05 12 4793 2498 67 0.250 1390 39
## 5 Alabama 2020-04-12 9 4486 4241 123 0.201 1743 56
## 6 Alabama 2020-04-19 6 3570 5610 201 0.168 1369 78statsbyweek %>% group_by(state) %>% summarise(n())## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 50 x 2
## state `n()`
## <chr> <int>
## 1 Alabama 29
## 2 Alaska 29
## 3 Arizona 36
## 4 Arkansas 30
## 5 California 36
## 6 Colorado 30
## 7 Connecticut 30
## 8 Delaware 30
## 9 Florida 31
## 10 Georgia 31
## # ... with 40 more rowstsplotter(statsbyweek %>% filter(state=="New York"),label="New York")
tsplotter(statsbyweek %>% filter(state=="California"),label="California")
tsplotter(statsbyweek %>% filter(state=="Texas"),label="Texas")
statsbyweek=as.data.frame(statsbyweek)lm(cases~hoaxsh,statsbyweek) %>% summary()##
## Call:
## lm(formula = cases ~ hoaxsh, data = statsbyweek)
##
## Residuals:
## Min 1Q Median 3Q Max
## -189328 -50914 -40048 7176 751613
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 50929 3108 16.388 < 2e-16 ***
## hoaxsh 11555 2380 4.855 1.33e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 108700 on 1544 degrees of freedom
## Multiple R-squared: 0.01504, Adjusted R-squared: 0.0144
## F-statistic: 23.57 on 1 and 1544 DF, p-value: 1.326e-06lm(cases~hoaxsh+factor(week),statsbyweek) %>% summary()##
## Call:
## lm(formula = cases ~ hoaxsh + factor(week), data = statsbyweek)
##
## Residuals:
## Min 1Q Median 3Q Max
## -199861 -37318 -9820 1098 668461
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.00 99956.85 0.000 0.99999
## hoaxsh 7865.20 2593.18 3.033 0.00246 **
## factor(week)2020-01-26 -2439.83 111758.05 -0.022 0.98259
## factor(week)2020-02-02 -95.32 107965.74 -0.001 0.99930
## factor(week)2020-02-09 1.00 106858.37 0.000 0.99999
## factor(week)2020-02-16 -254.24 106020.28 -0.002 0.99809
## factor(week)2020-02-23 -50.25 105363.77 0.000 0.99962
## factor(week)2020-03-01 -1014.28 102855.30 -0.010 0.99213
## factor(week)2020-03-08 -70.35 101086.35 -0.001 0.99944
## factor(week)2020-03-15 -133.49 100951.52 -0.001 0.99895
## factor(week)2020-03-22 236.01 100952.16 0.002 0.99813
## factor(week)2020-03-29 2530.42 100953.13 0.025 0.98001
## factor(week)2020-04-05 6423.98 100953.96 0.064 0.94927
## factor(week)2020-04-12 10540.03 100954.06 0.104 0.91686
## factor(week)2020-04-19 14195.65 100954.80 0.141 0.88819
## factor(week)2020-04-26 18636.04 100953.93 0.185 0.85357
## factor(week)2020-05-03 13982.43 101011.43 0.138 0.88992
## factor(week)2020-05-10 10506.78 101111.51 0.104 0.91725
## factor(week)2020-05-17 21445.90 101000.18 0.212 0.83187
## factor(week)2020-05-24 27687.45 100972.27 0.274 0.78396
## factor(week)2020-05-31 33274.50 100958.75 0.330 0.74176
## factor(week)2020-06-07 37034.00 100956.02 0.367 0.71380
## factor(week)2020-06-14 36945.13 100972.52 0.366 0.71450
## factor(week)2020-06-21 44614.05 100956.18 0.442 0.65861
## factor(week)2020-06-28 48322.28 100966.91 0.479 0.63230
## factor(week)2020-07-05 57900.43 100956.69 0.574 0.56638
## factor(week)2020-07-12 65139.58 100963.23 0.645 0.51891
## factor(week)2020-07-19 74518.32 100962.63 0.738 0.46058
## factor(week)2020-07-26 86415.02 100952.94 0.856 0.39214
## factor(week)2020-08-02 94234.49 100953.14 0.933 0.35074
## factor(week)2020-08-09 100693.59 100955.54 0.997 0.31873
## factor(week)2020-08-16 108173.80 100953.17 1.072 0.28411
## factor(week)2020-08-23 114411.68 100952.54 1.133 0.25726
## factor(week)2020-08-30 117968.07 100958.41 1.168 0.24280
## factor(week)2020-09-06 118457.69 100986.50 1.173 0.24098
## factor(week)2020-09-13 124743.57 100979.23 1.235 0.21690
## factor(week)2020-09-20 114588.39 101244.89 1.132 0.25790
## factor(week)2020-09-27 140013.96 100959.49 1.387 0.16570
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 99960 on 1508 degrees of freedom
## Multiple R-squared: 0.1859, Adjusted R-squared: 0.1659
## F-statistic: 9.304 on 37 and 1508 DF, p-value: < 2.2e-16lm(cases~hoaxsh++factor(state)+factor(week),statsbyweek) %>% summary()##
## Call:
## lm(formula = cases ~ hoaxsh + +factor(state) + factor(week),
## data = statsbyweek)
##
## Residuals:
## Min 1Q Median 3Q Max
## -264367 -23041 593 22221 456332
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1002 70567 -0.014 0.988669
## hoaxsh 3788 1863 2.033 0.042192 *
## factor(state)Alaska -52626 17974 -2.928 0.003465 **
## factor(state)Arizona 41125 17193 2.392 0.016885 *
## factor(state)Arkansas -24748 17843 -1.387 0.165651
## factor(state)California 223775 17186 13.021 < 2e-16 ***
## factor(state)Colorado -19744 17833 -1.107 0.268403
## factor(state)Connecticut -15063 17829 -0.845 0.398342
## factor(state)Delaware -45578 17878 -2.549 0.010892 *
## factor(state)Florida 200328 17695 11.321 < 2e-16 ***
## factor(state)Georgia 59035 17710 3.333 0.000879 ***
## factor(state)Hawaii -47306 17881 -2.646 0.008243 **
## factor(state)Idaho -40063 17996 -2.226 0.026152 *
## factor(state)Illinois 78867 17185 4.589 4.83e-06 ***
## factor(state)Indiana -3130 17831 -0.176 0.860678
## factor(state)Iowa -19088 17868 -1.068 0.285580
## factor(state)Kansas -31846 17840 -1.785 0.074457 .
## factor(state)Kentucky -28872 17843 -1.618 0.105857
## factor(state)Louisiana 18274 17849 1.024 0.306101
## factor(state)Maine -50864 17993 -2.827 0.004766 **
## factor(state)Maryland 10304 17871 0.577 0.564306
## factor(state)Massachusetts 40510 17291 2.343 0.019276 *
## factor(state)Michigan 14787 17827 0.829 0.406972
## factor(state)Minnesota -15911 17827 -0.893 0.372243
## factor(state)Mississippi -17436 17829 -0.978 0.328263
## factor(state)Missouri -15275 17829 -0.857 0.391718
## factor(state)Montana -50312 17999 -2.795 0.005255 **
## factor(state)Nebraska -24086 17490 -1.377 0.168685
## factor(state)Nevada -25351 17833 -1.422 0.155373
## factor(state)New Hampshire -43303 17711 -2.445 0.014602 *
## factor(state)New Jersey 89083 17707 5.031 5.48e-07 ***
## factor(state)New Mexico -40573 17826 -2.276 0.022992 *
## factor(state)New York 273568 17695 15.461 < 2e-16 ***
## factor(state)North Carolina 24713 17703 1.396 0.162942
## factor(state)North Dakota -47733 17826 -2.678 0.007498 **
## factor(state)Ohio 7729 17831 0.433 0.664720
## factor(state)Oklahoma -28669 17827 -1.608 0.108011
## factor(state)Oregon -37723 17693 -2.132 0.033171 *
## factor(state)Pennsylvania 31036 17828 1.741 0.081916 .
## factor(state)Rhode Island -34009 17715 -1.920 0.055089 .
## factor(state)South Carolina -1035 17833 -0.058 0.953744
## factor(state)South Dakota -45387 17829 -2.546 0.011008 *
## factor(state)Tennessee 12180 17826 0.683 0.494573
## factor(state)Texas 195074 17365 11.234 < 2e-16 ***
## factor(state)Utah -20935 17593 -1.190 0.234257
## factor(state)Vermont -48885 17893 -2.732 0.006368 **
## factor(state)Virginia 9484 17835 0.532 0.594974
## factor(state)Washington 1003 17192 0.058 0.953470
## factor(state)West Virginia -48636 17997 -2.702 0.006962 **
## factor(state)Wisconsin -1503 17272 -0.087 0.930670
## factor(state)Wyoming -50667 17829 -2.842 0.004547 **
## factor(week)2020-01-26 -86364 77154 -1.119 0.263164
## factor(week)2020-02-02 -63005 74656 -0.844 0.398845
## factor(week)2020-02-09 -81689 73928 -1.105 0.269351
## factor(week)2020-02-16 -68464 73377 -0.933 0.350953
## factor(week)2020-02-23 -58332 72946 -0.800 0.424036
## factor(week)2020-03-01 -62159 71303 -0.872 0.383489
## factor(week)2020-03-08 -12585 70148 -0.179 0.857643
## factor(week)2020-03-15 -6066 70060 -0.087 0.931016
## factor(week)2020-03-22 -5266 70060 -0.075 0.940094
## factor(week)2020-03-29 -2647 70060 -0.038 0.969869
## factor(week)2020-04-05 1451 70061 0.021 0.983483
## factor(week)2020-04-12 5590 70061 0.080 0.936414
## factor(week)2020-04-19 9398 70061 0.134 0.893308
## factor(week)2020-04-26 13656 70061 0.195 0.845486
## factor(week)2020-05-03 13366 70101 0.191 0.848810
## factor(week)2020-05-10 13360 70173 0.190 0.849033
## factor(week)2020-05-17 20290 70093 0.289 0.772264
## factor(week)2020-05-24 24822 70073 0.354 0.723218
## factor(week)2020-05-31 29094 70064 0.415 0.678023
## factor(week)2020-06-07 32454 70062 0.463 0.643278
## factor(week)2020-06-14 34099 70073 0.487 0.626599
## factor(week)2020-06-21 40060 70062 0.572 0.567563
## factor(week)2020-06-28 45011 70069 0.642 0.520725
## factor(week)2020-07-05 53427 70063 0.763 0.445850
## factor(week)2020-07-12 61475 70067 0.877 0.380427
## factor(week)2020-07-19 70792 70066 1.010 0.312495
## factor(week)2020-07-26 81185 70060 1.159 0.246730
## factor(week)2020-08-02 89061 70060 1.271 0.203860
## factor(week)2020-08-09 96031 70062 1.371 0.170692
## factor(week)2020-08-16 103009 70060 1.470 0.141699
## factor(week)2020-08-23 109055 70060 1.557 0.119782
## factor(week)2020-08-30 113742 70064 1.623 0.104718
## factor(week)2020-09-06 116552 70083 1.663 0.096516 .
## factor(week)2020-09-13 122379 70078 1.746 0.080965 .
## factor(week)2020-09-20 120611 70270 1.716 0.086304 .
## factor(week)2020-09-27 135928 70064 1.940 0.052567 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 68440 on 1459 degrees of freedom
## Multiple R-squared: 0.6307, Adjusted R-squared: 0.609
## F-statistic: 28.98 on 86 and 1459 DF, p-value: < 2.2e-16library(plm)
plm(cases~hoaxsh+factor(week)+factor(state),statsbyweek,
index=c("state","week"),
model="within",
effect="twoways") %>% summary()## Twoways effects Within Model
##
## Call:
## plm(formula = cases ~ hoaxsh + factor(week) + factor(state),
## data = statsbyweek, effect = "twoways", model = "within",
## index = c("state", "week"))
##
## Unbalanced Panel: n = 50, T = 29-37, N = 1546
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -264367.42 -23040.53 592.79 22221.48 456331.70
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## hoaxsh 3788.3 1863.0 2.0334 0.04219 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 6.8535e+12
## Residual Sum of Squares: 6.8341e+12
## R-Squared: 0.0028259
## Adj. R-Squared: -0.055952
## F-statistic: 4.13474 on 1 and 1459 DF, p-value: 0.042192Unit roots
obs=100
eps=rnorm(obs)
y99=eps
y100=eps
yM99=eps
for(i in 2:obs){
y99[i] = y99[i-1] *.95 +eps[i]
yM99[i]=-yM99[i-1]*.99+eps[i]
y100[i]= y100[i-1]*1+eps[i]
}
sdf=data.frame(y99,y100,yM99,eps,period=1:obs)
#library(latex2exp)
ggplot(sdf,aes(x=period))+geom_line(aes(y=y99,color="rho=0.99"))+
geom_line(aes(y=y100,color="rho=1"))+
geom_line(aes(y=yM99,color="rho=-.99"))+
theme_minimal()+ylab("y")
library(urca)## Warning: package 'urca' was built under R version 4.0.2 ur.df(df$cases,type="none",lags=1) %>% summary()##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.02151 0.00000 0.00000 0.00000 0.07106
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 0.0004516 0.0006910 0.654 0.514
## z.diff.lag 0.9805725 0.0133827 73.272 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.004085 on 667 degrees of freedom
## Multiple R-squared: 0.9468, Adjusted R-squared: 0.9467
## F-statistic: 5938 on 2 and 667 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: 0.6536
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62 ur.df(df$lnindex,type="none",lags=1) %>% summary()##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.343e-04 -2.643e-05 4.240e-06 4.131e-05 1.922e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -2.155e-05 2.703e-05 -0.797 0.426
## z.diff.lag 9.924e-01 5.596e-03 177.334 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.414e-05 on 667 degrees of freedom
## Multiple R-squared: 0.9812, Adjusted R-squared: 0.9811
## F-statistic: 1.739e+04 on 2 and 667 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -0.7971
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62 ur.df(diff(df$cases,1),type="none",lags=1) %>% summary()##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.02330 0.00000 0.00000 0.00000 0.04392
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.036593 0.007388 -4.953 9.26e-07 ***
## z.diff.lag 0.604696 0.031607 19.132 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.003285 on 666 degrees of freedom
## Multiple R-squared: 0.3567, Adjusted R-squared: 0.3547
## F-statistic: 184.6 on 2 and 666 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -4.9534
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62 ur.df(diff(df$lnindex,1),type="none",lags=1) %>% summary()##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.236e-04 -3.079e-05 3.980e-06 4.133e-05 1.963e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.010977 0.005233 -2.098 0.0363 *
## z.diff.lag 0.195464 0.038082 5.133 3.75e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.28e-05 on 666 degrees of freedom
## Multiple R-squared: 0.04215, Adjusted R-squared: 0.03927
## F-statistic: 14.65 on 2 and 666 DF, p-value: 5.92e-07
##
##
## Value of test-statistic is: -2.0976
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62df=df %>% arrange(week) %>% mutate(Dlnindex=lnindex-dplyr::lag(lnindex),
Dcases=cases-dplyr::lag(cases) ,
DDlnindex=Dlnindex-dplyr::lag(Dlnindex),Dlockshare=lockshare-dplyr::lag(lockshare))
lm(Dlnindex~Dcases+t,df) %>% summary() ##
## Call:
## lm(formula = Dlnindex ~ Dcases + t, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.107e-03 -9.941e-05 4.439e-05 1.487e-04 1.041e-03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.429e-04 2.415e-05 5.918 5.20e-09 ***
## Dcases -2.316e-02 7.258e-04 -31.914 < 2e-16 ***
## t 5.269e-07 6.490e-08 8.119 2.28e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.000305 on 667 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.6065, Adjusted R-squared: 0.6053
## F-statistic: 513.9 on 2 and 667 DF, p-value: < 2.2e-16lm(Dlnindex~Dcases+t+Dlockshare,df) %>% summary()##
## Call:
## lm(formula = Dlnindex ~ Dcases + t + Dlockshare, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0011149 -0.0001001 0.0000414 0.0001472 0.0010273
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.401e-04 2.404e-05 5.831 8.61e-09 ***
## Dcases -2.311e-02 7.221e-04 -32.010 < 2e-16 ***
## t 5.400e-07 6.471e-08 8.345 4.10e-16 ***
## Dlockshare -1.253e-05 4.354e-06 -2.878 0.00412 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0003034 on 666 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.6113, Adjusted R-squared: 0.6095
## F-statistic: 349.1 on 3 and 666 DF, p-value: < 2.2e-16lm(Dlnindex~Dcases+t+Dlockshare,df) %>% summary()##
## Call:
## lm(formula = Dlnindex ~ Dcases + t + Dlockshare, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0011149 -0.0001001 0.0000414 0.0001472 0.0010273
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.401e-04 2.404e-05 5.831 8.61e-09 ***
## Dcases -2.311e-02 7.221e-04 -32.010 < 2e-16 ***
## t 5.400e-07 6.471e-08 8.345 4.10e-16 ***
## Dlockshare -1.253e-05 4.354e-06 -2.878 0.00412 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0003034 on 666 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.6113, Adjusted R-squared: 0.6095
## F-statistic: 349.1 on 3 and 666 DF, p-value: < 2.2e-16lm(Dlnindex~dplyr::lag(Dlnindex)+Dcases+t+Dlockshare,df) %>% summary() ##
## Call:
## lm(formula = Dlnindex ~ dplyr::lag(Dlnindex) + Dcases + t + Dlockshare,
## data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.875e-04 -3.296e-05 -7.900e-07 3.513e-05 1.848e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.998e-06 5.098e-06 0.588 0.55673
## dplyr::lag(Dlnindex) 9.557e-01 7.810e-03 122.365 < 2e-16 ***
## Dcases -1.286e-03 2.325e-04 -5.530 4.6e-08 ***
## t 3.859e-08 1.400e-08 2.756 0.00602 **
## Dlockshare -1.382e-05 8.985e-07 -15.377 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.26e-05 on 664 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.9835, Adjusted R-squared: 0.9834
## F-statistic: 9894 on 4 and 664 DF, p-value: < 2.2e-16lm(Dlnindex~dplyr::lag(Dlnindex)+dplyr::lag(Dlnindex,2)+Dcases+dplyr::lag(Dcases)+dplyr::lag(Dcases,2)+t+Dlockshare+dplyr::lag(Dlockshare)+dplyr::lag(Dlockshare,2),df) %>% summary() ##
## Call:
## lm(formula = Dlnindex ~ dplyr::lag(Dlnindex) + dplyr::lag(Dlnindex,
## 2) + Dcases + dplyr::lag(Dcases) + dplyr::lag(Dcases, 2) +
## t + Dlockshare + dplyr::lag(Dlockshare) + dplyr::lag(Dlockshare,
## 2), data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.264e-04 -3.238e-05 -2.604e-06 3.437e-05 1.893e-04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.374e-06 4.565e-06 0.301 0.7634
## dplyr::lag(Dlnindex) 7.911e-01 3.793e-02 20.855 < 2e-16 ***
## dplyr::lag(Dlnindex, 2) 1.854e-01 3.743e-02 4.954 9.27e-07 ***
## Dcases -7.495e-04 1.100e-03 -0.681 0.4960
## dplyr::lag(Dcases) -3.192e-03 1.444e-03 -2.210 0.0275 *
## dplyr::lag(Dcases, 2) 3.703e-03 7.344e-04 5.043 5.94e-07 ***
## t 2.186e-08 1.270e-08 1.721 0.0857 .
## Dlockshare -1.036e-05 8.940e-07 -11.586 < 2e-16 ***
## dplyr::lag(Dlockshare) -9.179e-06 1.167e-06 -7.867 1.49e-14 ***
## dplyr::lag(Dlockshare, 2) -3.171e-06 1.449e-06 -2.189 0.0290 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.585e-05 on 658 degrees of freedom
## (3 observations deleted due to missingness)
## Multiple R-squared: 0.987, Adjusted R-squared: 0.9868
## F-statistic: 5546 on 9 and 658 DF, p-value: < 2.2e-16# Time Series
#< load libraries
library(foreign)
#< GDP Japan
library(haven)
gdpjp <-read_dta("data/gdp_JP_etc.dta")
library(zoo)
library(DataCombine)
library(quantmod)
library(tseries)
gdpjp["L1lngdp"]=Lag(gdpjp$lngdp,1)
gdpjp["L1lngdp"]=Lag(gdpjp$lngdp,1)
summary(lm(lngdp~L1lngdp ,gdpjp))
summary(arma(gdpjp$lngdp, order = c(1, 0)))
summary(arma(gdpjp$lngdp, order = c(2, 0)))
summary(lm(lngdp~L1lngdp+time ,gdpjp))
gdpjp["Dlngdp"]<-c(NA,diff(gdpjp$lngdp, differences=1))
#>
#< Dickey Fuller
library(urca)
df=ur.df(gdpjp$lngdp,type="trend",lags=0)
summary(df)
summary(ur.df(diff(gdpjp$lngdp,1),type="trend",lags=0))
summary(ur.df(diff(gdpjp$lngdp,1),type="trend",lags=1))
summary(ur.df(gdpjp$lngdp,type="trend",lags=1))
summary(ur.df(gdpjp$lngdp,type="trend",lags=5))
summary(ur.df(gdpjp$lngdp,type="trend",lags=3))
summary(ur.df(diff(gdpjp$lngdp,1),type="trend",lags=3))
#>
#< Oragne juice
oj <-read_dta("data/oj.dta")
oj = na.omit(oj)
oj["lnp"]=log(oj$ppioj/oj$pwfsa *100)
summary(ur.df(oj$fdd,type="trend",lags=12))
summary(ur.df(oj$lnp,type="trend",lags=12))
summary(ur.df(diff(oj$lnp,1),type="trend",lags=12))
summary(lm(diff(oj$lnp,1)~oj$fdd[-1]))
ojm=lm(diff(oj$lnp)~oj$fdd[-1])
library(sandwich)
library(lmtest)
coeftest(ojm, vcov. = NeweyWest)
#>