10
votes
Accepted
Reasons for negative autocorrelation
Looking at transaction prices, they would occur at the market bid if the active part is a seller, and at the ask if the active part is a buyer. With a random flow of sellers and buyers, the price will ...
- 1,352
4
votes
Accepted
Is an autocorrelation of the abs returns just a consequence of the volatility burst?
I think @zer0hedge has constructed a clever example by which to demonstrate what is implied by the stylized fact by which volatility begets volatility.
It is correct to conclude volatility bursts are ...
- 2,985
4
votes
Interpreting ACF
You need to compute the autocorrelation of the log returns $r_t$, not of the prices, $p_t$. The relationship of the log return series to the price series is
$$
r_t = \log \frac{p_t}{p_{t-1}}
$$
The ...
- 5,891
3
votes
Variance Ratio Test in R
TL;DR: the test statistic's distribution is $N(0,1)$
A bit more information about the Automatic Variance Ratio Test:
$H_0$: ${\Delta}r_t$ is serially uncorrelated (where ${\Delta}r_t=r_t-r_{t-1}$)
$...
- 735
3
votes
Accepted
Running an autocorrelation with blanks?
One option is just to fill them in - interest rates don't usually jump around, so interpolating from surrounding data would be unsurprising. If you want to know what effect that is having, by all ...
- 3,669
3
votes
Do EWMA weights remove autocorrelation in asset returns?
EWMA (and other sort of moving averages) introduces positive autocorrelation into otherwise uncorrelated returns. The fitted values of EWMA are linear combinations of past returns, and the constituent ...
- 2,706
3
votes
How to use autocorrelation plot to interpret time series data?
Just by looking at the graphs, I'd say:
Unit root
Constant series
Seasonality
AR model
No AC
No AC
- 707
3
votes
Accepted
Predictive power of lagged features
In its simplest terms, imagine you were just using the yield curve as your single predictor of recessions. Suppose (horribly simplistically) that curve inversions tend to signal downturns in 12-18 ...
- 5,041
3
votes
Auto-covariance function of station time series
Hi: Subtract $k$ from $z_t$ and add $k$ to $z_{t-k}$. Then you have $cov(z_{t-k,} z_{t})$ which by definition is $\gamma_{-k}$. But, by stationarity, this has to be equal to $cov(z_{t}, z_{t-k})= \...
- 1,082
3
votes
Accepted
Autocorrelation in the GARCH model residuals
You should check for autocorrelation. However, its presence does not necessarily mean your model will produce inaccurate figures. The ARCH family of models were developed to help analyze the ...
- 341
3
votes
Does GARCH derived variance explain the autocorrelation in a time series?
What is the mathematical basis to say that $u^{2}_{t}/\sigma_{t}^{2}$ will exhibit little auto-correlation in the series?
Let's $r_{t}$ be a series of returns and let's assume (Assumption I) it ...
- 2,552
3
votes
Detecting stochastic volatility
I'm not a time series expert but one idea occurs to me: look at the distribution of the increments if Z(t). If the w are stochastic , that distribution should have fat tails relative to the ...
- 16.5k
3
votes
Accepted
How does autocorrelation bias annualizing variance?
In Andrew W. Lo's paper, The statistics of Sharpe Ratios (2002) he derives the variance of non-IID returns (returns that can exhibit serial correlation) under the assumption of (covariance) stationary ...
- 4,176
2
votes
Stationary Process with autocorrelation in Variance; square root rule
You are correct in that the series is not stationary. The ADF test isn't designed to test for stationarity outside the center of location. You are not going to be able to use the square root rule to ...
- 4,359
2
votes
Is an autocorrelation of the abs returns just a consequence of the volatility burst?
Your code basically implements the assumption that you cited:
The volatility of return processes is not constant with respect to
time.
Whether it's a single burst or some kind of a fancy ...
2
votes
Is an autocorrelation of the abs returns just a consequence of the volatility burst?
Such volatility pattern is a well-known stylized fact of financial time series (see Cont, Rama. Empirical properties of asset returns: stylized facts and statistical issues. (2001): 223-236 for more ...
- 1,219
2
votes
Accepted
Turning a covariance sum into an integral
Note that the function $f$ only depends on $|t-u|$, meaning it is actually symmetric: $f(x)=f(-x)$. Doing the change of variable $\tau:=t-u$:
$$\begin{align}
\int_0^Tdu\int_0^Tf(t-u)dt
&=\int_0^...
- 7,959
2
votes
Is there an issue with estimating future returns from autocorrelated returns?
If you are predicting the return from time "i" to time "i+l" then you cannot use any information beyond time "i" to train your model. As it appears you are getting returns from "i-5" to "i" and ...
- 151
2
votes
Accepted
Monte Carlo simulations of correlated stocks by Geometric Brownian motion
Let $n$ be the number of stocks (here $n=3$)
Let $T$ be the number of sequential returns to generate (for example $T=12$ if you want to generate a year's worth of monthly returns)
Let $M$ be the ...
- 10.9k
2
votes
Should a stock with high return autocorrelation be weighted more heavily in a portfolio?
Hmm... some notable implicit assumptions made en passant here ;-) How persistent are these autocorrelations (ACs)? Let's unpick a little.
One obvious question is whether your AC process is strong ...
- 5,041
2
votes
What about autocorrelation and heteroskedasticity in Fama French?
If you face heteroskedasticity, you have to check if heteroskedasticity is conditional (e.g., with a Breush-Pagan Chi-square test). If so, you have to use White-corrected standard errors.
If you have ...
- 206
2
votes
Accepted
Show that $\text{Cov}[X_r,X_s]=\text{Cov}[X_{r+h},X_{s+h}]$ for $X_t=a+bZ_t+cZ_{t-2}.$
in method 1 you did not use the correct definition of the covariance. For two random variables $X$ and $Y$ we have that
$$
Cov(X, Y) = E[XY] - E[X]E[Y].
$$
Also, we can use that the covariance is ...
- 1,436
1
vote
Persistence and stationarity together in volatility analysis
ADF tests for a unit root. Autocorrelation function of a unit root process does not make sense. For example let
$$y_{t+1}=y_t+\epsilon_{t+1}$$
Here $\epsilon_t$ is i.i.d white noise. Then the one ...
- 1,692
1
vote
Running an autocorrelation with blanks?
Are you dealing with overnight rates, such as Fed Funds?
In such cases the same rate continues to be paid while the markets are closed. So for example if FF is X on Friday, it means you will earn X ...
- 10.9k
1
vote
How to use autocorrelation plot to interpret time series data?
There is a multitude of texts which answer this question the easiest and free source is Rob Hyndmans from Monash Universities online text on forecasting, https://otexts.com/fpp2/, the topic is covered ...
- 304
1
vote
Autocorrelation and frequency of occurence
I recently had trouble with a similar concept and I managed to develop a proof that related probability of successive occurrence with autocorrelation. Interpreting Autocorrelation as probability. Let ...
- 187
1
vote
Autocovariance of increments of a semimartingale
**please correct me if the math is wrong!!
I think upon breaking down the products $E(dX_tdX_s)$, we have the $dtds$, $dtdW_s$ terms which all turns out to be 0. It leaves $E(dW_tdW_s)$ which comes ...
- 609
1
vote
Interpreting ACF
ACF plot suggests there is autocorrelation which lasts for long time. The series is clearly not stationary. You may try differencing once - return time series, then plot boathouse ACF and PACF.
- 11
1
vote
Squared and Absolute Returns
Also, often we can assume the average of short-term returns in the long run to be zero, the historic volatility is equal to
$\hat{\sigma_T^2}=\frac{\sum_{i=1}^T{r_i^2}}{T-1}$. Sp to study the ...
- 177
1
vote
How to adjust regression for rolling returns?
It depends how large the overlapping interval is. Conceptually an infinite rolling window is equivalent to the level, and no one would suggest to 'regress on levels and apply Newey West'.
I think NW ...
- 4,307
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