library(Quandl)
library(xts)
library(vars)
library(lmtest)

### Data
pGold <- Quandl("BUNDESBANK/BBK01_WT5511", start_date="2010-01-01")
Gold <- xts(pGold$Value, order.by=pGold$Date)

bitcoin <- Quandl("BITCOIN/BITSTAMPUSD")
btc <- xts(bitcoin$'Weighted Price', order.by=bitcoin$Date)
drop <- which(btc > 10**6)
btc <- btc[-drop]; rm(drop)

### Plots
par(mfrow=c(2,1))
plot(log(btc))
plot(log(Gold))

plot(diff(log(btc)))
plot(diff(log(Gold)))
par(mfrow=c(1,1))

### Quick Granger Causality test
# Use differences in logs
d.l.Gold <- diff(log(Gold))
d.l.btc <- diff(log(btc))
dat <- na.omit(merge(d.l.Gold, d.l.btc))

# Console output from here on:

> VARselect(dat) # AIC: 4 lags
$selection
AIC(n)  HQ(n)  SC(n) FPE(n)
     4      4      1      4

$criteria
                   1             2             3             4             5             6             7             8             9            10
AIC(n) -1.444529e+01 -1.445135e+01 -1.446099e+01 -1.448978e+01 -1.448490e+01 -1.448642e+01 -1.447868e+01 -1.447276e+01 -1.446438e+01 -1.445322e+01
HQ(n)  -1.442900e+01 -1.442419e+01 -1.442296e+01 -1.444088e+01 -1.442514e+01 -1.441579e+01 -1.439719e+01 -1.438041e+01 -1.436116e+01 -1.433914e+01
SC(n)  -1.440331e+01 -1.438139e+01 -1.436304e+01 -1.436384e+01 -1.433098e+01 -1.430451e+01 -1.426879e+01 -1.423488e+01 -1.419851e+01 -1.415937e+01
FPE(n)  5.327073e-07  5.294907e-07  5.244134e-07  5.095320e-07  5.120251e-07  5.112516e-07  5.152244e-07  5.182883e-07  5.226560e-07  5.285245e-07

> grangertest(formula = d.l.Gold ~ d.l.btc, data = dat, order=4) #***
Granger causality test

Model 1: d.l.Gold ~ Lags(d.l.Gold, 1:4) + Lags(d.l.btc, 1:4)
Model 2: d.l.Gold ~ Lags(d.l.Gold, 1:4)
  Res.Df Df      F    Pr(>F)
1    634
2    638 -4 5.8054 0.0001362 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> grangertest(formula = d.l.btc ~ d.l.Gold, data = dat, order=4) #***
Granger causality test

Model 1: d.l.btc ~ Lags(d.l.btc, 1:4) + Lags(d.l.Gold, 1:4)
Model 2: d.l.btc ~ Lags(d.l.btc, 1:4)
  Res.Df Df      F    Pr(>F)
1    634
2    638 -4 4.6772 0.0009999 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


# Significant Granger Causality in both directions.