# NOT RUN {
## Simple Time Series: AirPassengers
D(AirPassengers) # 1st difference, same as fdiff(AirPassengers)
D(AirPassengers, -1) # Forward difference
Dlog(AirPassengers) # Log-difference
D(AirPassengers, 1, 2) # Second difference
Dlog(AirPassengers, 1, 2) # Second log-difference
D(AirPassengers, 12) # Seasonal difference (data is monthly)
D(AirPassengers, # Quasi-difference, see a better example below
rho = pwcor(AirPassengers, L(AirPassengers)))
head(D(AirPassengers, -2:2, 1:3)) # Sequence of leaded/lagged and iterated differences
# let's do some visual analysis
plot(AirPassengers) # Plot the series - seasonal pattern is evident
plot(stl(AirPassengers, "periodic")) # Seasonal decomposition
plot(D(AirPassengers,c(1,12),1:2)) # Plotting ordinary and seasonal first and second differences
plot(stl(window(D(AirPassengers,12), # Taking seasonal differences removes most seasonal variation
1950), "periodic"))
## Time Series Matrix of 4 EU Stock Market Indicators, recorded 260 days per year
plot(D(EuStockMarkets, c(0, 260))) # Plot series and annual differnces
mod <- lm(DAX ~., L(EuStockMarkets, c(0, 260))) # Regressing the DAX on its annual lag
summary(mod) # and the levels and annual lags others
r <- residuals(mod) # Obtain residuals
pwcor(r, L(r)) # Residual Autocorrelation
fFtest(r, L(r)) # F-test of residual autocorrelation
# (better use lmtest::bgtest)
modCO <- lm(QD1.DAX ~., D(L(EuStockMarkets, c(0, 260)), # Cochrane-Orcutt (1949) estimation
rho = pwcor(r, L(r))))
summary(modCO)
rCO <- residuals(modCO)
fFtest(rCO, L(rCO)) # No more autocorrelation
## World Development Panel Data
head(fdiff(num_vars(wlddev), 1, 1, # Computes differences of numeric variables
wlddev$country, wlddev$year)) # fdiff requires external inputs..
head(D(wlddev, 1, 1, ~country, ~year)) # Differences of numeric variables
head(D(wlddev, 1, 1, ~country)) # Without t: Works because data is ordered
head(D(wlddev, 1, 1, PCGDP + LIFEEX ~ country, ~year)) # Difference of GDP & Life Expectancy
head(D(wlddev, 0:1, 1, ~ country, ~year, cols = 9:10)) # Same, also retaining original series
head(D(wlddev, 0:1, 1, ~ country, ~year, 9:10, # Dropping id columns
keep.ids = FALSE))
# Dynamic Panel Data Models:
summary(lm(D(PCGDP,1,1,iso3c,year) ~ # Diff. GDP regressed on it's lagged level
L(PCGDP,1,iso3c,year) + # and the difference of Life Expanctancy
D(LIFEEX,1,1,iso3c,year), data = wlddev))
g = qF(wlddev$country) # Omitting t and precomputing g allows for
summary(lm(D(PCGDP,1,1,g) ~ L(PCGDP,1,g) + # a bit more parsimonious specification
D(LIFEEX,1,1,g), wlddev))
summary(lm(D1.PCGDP ~., # Now adding level and lagged level of
L(D(wlddev,0:1,1, ~ country, ~year,9:10),0:1, # LIFEEX and lagged differences rates
~ country, ~year, keep.ids = FALSE)[-1]))
## Using plm can make things easier, but avoid attaching or 'with' calls:
pwlddev <- plm::pdata.frame(wlddev, index = c("country","year"))
head(D(pwlddev, 0:1, 1, 9:10)) # Again differences of LIFEEX and PCGDP
PCGDP <- pwlddev$PCGDP # A panel-Series of GDP per Capita
head(D(PCGDP)) # Differencing the panel series
summary(lm(D1.PCGDP ~., # Running the dynamic model again ->
data = L(D(pwlddev,0:1,1,9:10),0:1, # code becomes a bit simpler
keep.ids = FALSE)[-1]))
# One could be tempted to also do something like this, but THIS DOES NOT WORK!!:
# -> a pseries is only created when subsetting the pdata.frame using $ or [[
summary(lm(D(PCGDP) ~ L(D(PCGDP,0:1)) + L(D(LIFEEX,0:1),0:1), pwlddev))
# To make it work, one needs to create pseries
LIFEEX <- pwlddev$LIFEEX
summary(lm(D(PCGDP) ~ L(D(PCGDP,0:1)) + L(D(LIFEEX,0:1),0:1))) # THIS WORKS !
## Using dplyr:
library(dplyr)
wlddev %>% group_by(country) %>%
select(PCGDP,LIFEEX) %>% fdiff(0:1,1:2) # Adding a first and second difference
wlddev %>% group_by(country) %>%
select(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year) # Also using t (safer)
wlddev %>% group_by(country) %>% # Dropping id's
select(year,PCGDP,LIFEEX) %>% D(0:1,1:2,year, keep.ids = FALSE)
# }
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