advanced-algorithmic-trading

384
## Carry out linear regression on the two price series
comb = lm(aAdj~bAdj)
> comb
Call:
lm(formula = aAdj ~ bAdj)
Coefficients:
(Intercept)
bAdj
11.039 1.213
In the linear regression where UNG is the independent variable the slope is given by 1.213.
The final task is to carry out the ADF test and determine whether there is any structural
cointegrating relationship:
## Now we perform the ADF test on the residuals,
## or "spread" of the model, using a single lag order
> adf.test(comb$residuals, k=1)
Augmented Dickey-Fuller Test
data: comb$residuals
Dickey-Fuller = -2.5413, Lag order = 1, p-value = 0.3492
alternative hypothesis: stationary
This analysis shows that there is not sufficient evidence to reject the null hypothesis of no
cointegrating relationship. However despite this it is instructive to continue implementing the
strategy with the hedging ratio calculated above for two reasons:
1. Any other potential cointegration-based analysis as derived from the CADF or the Johansen
test can be backtested using the following code since it has been written to be flexible
enough to cope with large cointegrated portfolios.
2. It is valuable to see how a strategy performs when there is insufficient evidence to reject
the null hypothesis. Perhaps the pair is still tradeable even though a relationship has not
been detected on this small dataset.
The trading strategy mechanism will now be outlined.
27.3 The Trading Strategy
In order to actually generate tradeable signals with a mean-reverting "spread" of prices from a
linear combination of ARNC and UNG a technique known as Bollinger Bands will be utilised.
Bollinger Bands involve taking a rolling simple moving average (SMA) of a price series and
then forming "bands" surrounding the series that are a scalar multiple of the rolling standard
deviation of the price series. The lookback period for the moving average and standard deviation
is identical. In essence they are an estimate of current volatility for a price series.