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Questions tagged [auto-correlation]

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0
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1answer
21 views

Auto-covariance function of station time series

How to show that for any stationary time series its auto-covariance function is symmetric about the origin, that is $\gamma_{k}=\gamma_{-k}$ where, $\gamma_k=cov(z_t,z_{t-k})$
3
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1answer
56 views

Autocovariance of increments of a semimartingale

Say that $X_t$ is an Itō process with \begin{equation} dX_t = \mu_t dt + \sigma_t dW_t \end{equation} where $\mu_t$ and $\sigma_t$ are adapted processes. Is it always true that \begin{equation} E[...
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3answers
72 views

Interpreting ACF

I am currently struggling with the interpretation of a price chart and the corresponding ACF graph. The question is, if there is momentum in the price of this asset. This is the corresponding price ...
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0answers
74 views

Why is the timings between trades of SPY precisely poised at criticality ? Can this fact be used for prediction?

Let's say we have a point process consisting of the times between trades of SPY for one particular trading day. Empirically, the auto-correlation never dies out to 0 and due to results in Long range ...
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0answers
216 views

Interpreting ACF/PACF of return series

Researching a return series on some currency pairs I grabbed 2 years worth of daily data and got to work trying to fit an ARIMA/GARCH model to it. Fitting the (log) return series: ...
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3answers
794 views

Is an autocorrelation of the abs returns just a consequence of the volatility burst?

In Pfaff's "Financial Risk Modelling and Portfolio Optimization with R" the following stylized facts are stated (among the others, p.26): The volatility of return processes is not constant with ...
3
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1answer
106 views

Detecting stochastic volatility

I have a time series extracted from a financial time series (so my series of prices is described by an arithmetic model $X(t)+Y(t)+Z(t)$, my series is $Z(t)$). I'm trying to model $Z(t)$ by a Levy ...
3
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2answers
168 views

Stationary Process with autocorrelation in Variance; square root rule

i am currently analyzing a time series of portfolio log returns and have conducted a ADF test with the result, that the series is stationary, but also found significant autocorrelation in the squared ...
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1answer
1k views

Variance Ratio Test in R

I would like to conduct a variance ratio test for a financial time series in order to examine whether I can apply the square root rule for the variance with the software R. I used the Automatic ...
7
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4answers
967 views

Reasons for negative autocorrelation

I am working with intraday stock prices. I have found that the autocorrelation between the returns is negative (significantly so, but the value is very small). I am aware of how to interpret negative ...
1
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2answers
620 views

How to adjust regression for rolling returns?

I have a predictor variable (x) and dependent variable (y). Both are monthly rolling annualized returns, which naturally induces significant autocorrelation in x and y. They both also fail to be ...
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0answers
139 views

VAR models for log-returns?

I am wondering if Vector Autoregression (and other autoregressive models) is a sound modelling for the daily (not high-frequency!) log-returns of time series from liquid financial markets. One can ...
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3answers
131 views

residual correlation remains after seasonal lag added

I'm attempting to model operating margins and a time plot indicated that the series may follow an autoregressive process. I initially fitted data to an AR(1) model and it appeared that residual ...
3
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3answers
2k views

Autocorrelation in the GARCH model residuals

I am estimating GARCH model for volatility calculation and as a data input I have used log first difference data (ln(a)-ln(b)). Usually I would check for autocorrelation in residuals(to check the ...
3
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1answer
153 views

volume-returns cross correlation interpretation

I want to find the relationship between volume and price returns in the S&P500. My first thought was to run a cross correlation in order to find who leads and who lags in the relation. It´s my ...
0
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1answer
1k views

When measuring autocorrelation should you use log returns or prices?

Let's say you want to measure intra day autocorrelation from 9:30 am to 1pm using 5-minute prices should you calculate the autocorrelation using raw prices or log returns (i.e. diff(log(prices)))? Can ...
5
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1answer
716 views

Measuring momentum as AR(1) process

I would like to measure the momentum in the price of a stock from the time the market opens until the time I trade each day. I want to use this momentum number in post-trade analysis (regression of ...
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0answers
891 views

Cointegration Test: Residual is stationary but not random?

I am testing cointegration relationship on various pairs of stocks by this following these steps. Test for I(1) on a pair of stocks, says X and Y, using Dickey-Fuller test. If both time series are ...
5
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2answers
2k views

How to annualise the volatility of non-iid returns?

I have a series of monthly log-returns; let's assume the log-returns are normally distributed, but exhibit significant serial correlation. In the case of normal, i.i.d. returns, I can annualize the ...
2
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1answer
924 views

How to interpret ACF and PACF plots

I just want to check that I am interpreting the ACF and PACF plots correctly: The data corresponds to the errors generated between the actual data points and the estimates generated using an AR(1) ...
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0answers
108 views

Rule of Thumb for minimum length of time series for AR(1) estimation

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data. More precisely I want to take non overlapping windows of length 1,2,3....n and ...
0
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2answers
118 views

Infinite autocorrelation - Unit root?

I have a time series of gold prices, on which I want to build an ARIMA model. The series is autocorrelated and if I can difference as often as I want, it always is. First: data: d1gold Dickey-Fuller ...
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2answers
444 views

Does GARCH derived variance explain the autocorrelation in a time series?

Given a time series $u_i$ of returns (where $i=1,\dotsc,t$), $\sigma_i$ is calculated from GARCH(1,1) as $$ \sigma_i^2=\omega+\alpha u_{i-1}^2 +\beta \sigma_{i-1}^2. $$ What is the mathematical ...
4
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1answer
2k views

How is the MA (moving average model) useful?

How is the MA model useful in modeling financial data, for example the stock indices? For example, from what i understand in the AR (auto-regressive) model portion, we can use the ADF test to check ...
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3answers
10k views

What does it mean by autocorrelation coefficient near 1?

It is said that the time series has a stochastic trend if the first autocorrelation coefficient will be near 1. Q1) What does it mean by the above statement? Q2) How do we calculate the first ...
4
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1answer
1k views

Need overlapping sample autocorrelation correction for calculating asset return correlations

I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, ...
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0answers
116 views

Insignificant or significant explanatory power over risk adjusted returns?

Currently iam working on my master thesis which is about risk adjusted returns in the Asia Pacific REIT market. The goal of the paper is to determine/find variables that conceive explanatory power ...
12
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1answer
837 views

rugarch: Joint estimation leads to different results

I want to fit an ARMA-GARCH model to my data using rugarch package in R. First of all, I look at the acf and pacf: ...
3
votes
1answer
308 views

Auto-correlation of GBM

The GBM is defined by $ dS(t) = \mu S(t)dt + \sigma S(t) dW_t, $ with analytical solution $ S(t^\prime) = S(t) exp\left[\left(\mu-\frac{\sigma^2}{2}\right)\left(t^\prime-t\right)+\sigma\left(W(t^\...
2
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3answers
568 views

Why do long-term equity return forecast models use dependent observations?

I've been reading up on different models used to forecast the equity risk premium, and I've seen a couple of papers that had questionable methods. For example, this paper by Javier Estrada goes into ...
3
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3answers
7k views

Squared and Absolute Returns

I've always wondered why do one use squared or absolute returns to determine if volatility modeling is required for the return series? We understand that there are various tests for its ...
9
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1answer
481 views

Is there a closed-form solution for the partial autocorrelation function of a Markov regime-switching process?

Consider a Markov Regime-switching process $X_{t}$ with $k$ regimes represented by $s_{t}$ such that $$X_{t}=\mu\left(s_{t}\right)+\epsilon_{t}$$ and $$\epsilon_{t}\sim N\left(0,\sigma^{2}\left(s_{...
2
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1answer
179 views

Good reference on sample autocorrelation?

I'm not a statistician but I'm writing my thesis on mathematical finance and I think it would be neat to have a short section about independence of stock returns. I need to get better understanding ...
5
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1answer
553 views

What is the correct procedure to choose the lag when preforming Johansen cointegration test?

When preforming Johansen cointegration test for 2 time series (the simple case) you need to decide the lag you want to use. Doing the test for different lag levels returns different results: for some ...
7
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1answer
707 views

Are shorter holding period strategies better?

Consider two statistically identical strategies (identical information ratios, sample size, ratio of transaction costs to total profit, etc.) except that one has a much shorter average holding period. ...
6
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2answers
7k views

Who cares about autocorrelation?

There is much in the literature about time-series and the problem of auto-correlation. Unfortunately the issue of why auto-correlation is actually troublesome is glossed over, and methods for testing ...
13
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1answer
8k views

Time Series Regression with Overlapping Data

I am seeing a regression model which is regressing Year-on-Year stock index returns on lagged (12 months) Year-on-Year returns of the same stock index, credit spread (difference between monthly mean ...
19
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2answers
890 views

How do you correct Max Draw-Down for auto-correlation?

When returns are auto-correlated, calculating a Sharpe ratio := $\frac {mean(x)}{\sqrt{var(x)}}$, (where $x$ are the returns) is complicated, but basically solved (see, e.g. Lo (2005)). Without the ...