1. Motivation A stock's idiosyncratic-return volatility is the root-mean-squared error, $\mathit{ivol}_{n,t} = \sqrt{ \sfrac{1}{D_t} \cdot \sum_{d_t=1}^{D_t} \varepsilon_{n,d_t}^2}$, from the daily regression \begin{align} r_{n,d_t} = \alpha + … [Continue reading]

# Impulse-Response Functions for VARs

1. Motivating Example If you regress the current quarter's inflation rate, $x_t$, on the previous quarter's rate using data from FRED over the period from Q3-1987 to Q4-2014, then you get the AR(1) point estimate, \begin{align} x_t = … [Continue reading]

# Bias in Time-Series Regressions

1. Motivation How persistent has IBM's daily trading volume been over the last month? How persistent have Apple's monthly stock returns been over the last $5$ years of trading? What about the US's annual GDP growth over the last century? To answer … [Continue reading]

# When Can Arbitrageurs Identify a Sporadic Pricing Error?

1. Motivation Imagine you're an arbitrageur and you see a sequence of abnormal returns: \begin{align} \mathit{ra}_t \overset{\scriptscriptstyle \mathrm{iid}}{\sim} \begin{cases} +1 &\text{w/ prob } \sfrac{1}{2} \cdot (1 + \alpha) \\ -1 … [Continue reading]

# Why Not Fourier Methods?

1. Motivation There are many ways that you might measure the typical horizon of a stock's demand shocks. For instance, Fourier methods might at first appear to be a promising approach, but first impressions can be deceiving. Here's why: spikes in … [Continue reading]