A sequence of events measured at disrete points in time.

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3
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0answers
187 views

Fitting a non linear AR + GARCH(1,1)-M model

I want to fit the following model to a time series: $$ y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\alpha_{2}y_{t-1}^{2}+\lambda h_{t}+\varepsilon_{t} $$ $$ ...
2
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3answers
352 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 ...
2
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2answers
916 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 ...
2
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2answers
3k views

Calculating Portfolio Skewness & Kurtosis

I need to calculate the skewness and kurtosis of 2 asset portfolio, can someone please help me with the formulas and definition of terms? Thank you. I have been using the matrices method and I am not ...
2
votes
3answers
461 views

Time Series or Regression

I'd like to research the impact of certain events and characteristics on the liquidity of the stocks over time. I've got a sample of 200 stocks and I use several measures of liquidity (Amihud, Bid-Ask ...
2
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3answers
125 views

Calibration of a GBM - what should dt be?

I have a time series of daily data that I want to calibrate GBM parameters $\mu$ and $\sigma$ to. Using the discretized solution $$ S_{t_{i+1}} = S_{t_i}\exp\left(\left(\mu - ...
2
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2answers
157 views

Intraday Data - Stylized Facts?

Can someone give an overview or literature on Intraday Data Stylized Facts? In particular for equity market returns or exchange rates.
2
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3answers
744 views

Analyze raw tick data

I'd like to work with raw tick data and naturally this data is unevenly spaced (for example, a couple of quotes are at the same second etc.) For example ...
2
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1answer
371 views

Is there a measure for the 'degree' of cointegration

Is there a standard (or maybe even intuitive?) way of ranking pairs of cointegrated time series so that one could make statements like the following: ...
2
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1answer
214 views

Picking from two correlated distributions

Can anyone provide a simple example of picking from two distributions, such that the two generated time series give a specified value of Pearson's correlation coefficient? I would like to do this in ...
2
votes
1answer
228 views

Testing for stationarity in large sample sizes

I keep struggling with testing 9 samples if they are stationary. Each of these samples is a real valued time series with 714.000 values. If I use the KPSS test with the each compleete sample set, the ...
2
votes
3answers
463 views

What data transformations to use in regression of credit spreads on equity prices?

Clearly there is a strong relationship between credit spreads and equity prices (both theoretically and empirically). But how would one go about formulating a regression which seeks to explain this ...
2
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2answers
112 views

What is the best way of updating data while using Empirical Mode Decomposition to analyze

I have a question about EMD updating new data points. For an entire time series, from beginning to the end, the EMD preforms quite good using the cubic spline function. The problem happens when new ...
2
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1answer
167 views

Stress Testing Methods

I'm working on the following task: Given quarterly data: a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages a slew of ...
2
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2answers
110 views

What impact does arbitrage have on realised volatility estimates?

Doing some research modeling/estimating volatility in the bitcoin market. There is quite a bit of scope for arbitrage within crypto-currency markets. Wonder if this has any impact on my volatility ...
2
votes
1answer
358 views

Techniques for forecasting short-frame data?

I'm having a problem in which a time series of 24 data points is given to forecast the next 12 data points. This 24 data points might be sparse (many are missing). Do you have any suggestion on what ...
2
votes
1answer
39 views

Two correlated time series - driver and follower

Say that there are two time series of highly correlated stocks one of which is the driver and the second one follows the first one. What mathematical meassure of formula would you use to identify ...
2
votes
1answer
79 views

ARIMA model, cannot get rid of low order ACF spike

I've gone through all the steps to fit a good ARIMA model - I plotted the data, I looked at the ADF tests, I looked at the ACF plot with no AR and MA terms just a constants. I came up with an ...
2
votes
1answer
48 views

What are the properties of the Expected Shortall measure when split in multiple time periods?

Suppose I have a single time series of losses $L$ that consists of two sub-parts $L_1$ and $L_2$. Is there a relationship that relates the expected shortfall of $L$ to the expected shortfall of $L_1, ...
2
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3answers
91 views

how to back out levels from a forecast of differenced series

I have a non-stationary series of bond yields $x_{t}$ that are logged and differenced $$y_{t}\equiv ln\left(x_{t}\right)-ln\left(x_{t-4}\right) $$ From that, I get a series of forecasted values ...
2
votes
1answer
260 views

How should we select efficiently orders parameters in time series modelling?

A common way to select orders parameters (ex: to choose the number of AR terms to be included in the model ) in time series modelling is to rely on some Information Criteria (AIC, BIC, Hannan ...
2
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1answer
661 views

Counterintuitive time varying Beta with Kalman filter

If you're used to play with R, you'll enjoy the following reproducible code: ...
2
votes
1answer
160 views

Event studies using revenue data vs. measuring abnormal returns

This may be a silly question, but does there exist a methodology for examining the impact of "events" on companies that are not publicly traded? I suppose it would look at abnormal revenues rather ...
2
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2answers
189 views

How to synchronize put and call option-data?

I recently retrieved a large amount of European option data, for call and put prices, from OptionMetrics. Doing so for the same time period I get a file consisting of 62558 rows of call prices & ...
2
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1answer
311 views

Stepwise Cointegration

This is more of a general question at this point, but if my thought process makes sense I will follow up with an R implementation. I have read a number of papers on cointegration analysis for pairs ...
2
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1answer
632 views

Predict Quadratic Trend in Time Series

Can anyone kindly point out if I made any mistakes in making predictions using quadratic regression model in time series? I called the predict() function with the appropriate data vector and model, ...
2
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2answers
152 views

What are the proper metrics to look at for checking discrepancies in these two time series

I am obtaining bid/ask price and volume market data from two different sources for the same ticker and for the same day and checking to see that at time intervals X they are "roughly the same". The ...
2
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3answers
575 views

How to annualize dividends paid at varying intervals?

I am attempting to write a function that will calculate the annualized rate of return for individual dividends made by illiquid investments. These dividends are paid at varying intervals and the ...
2
votes
1answer
149 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 ...
2
votes
1answer
124 views

How to reconstruct a discontinued economic time series such as the Fed's CP rate?

The old 3-Month Commercial Paper Rate (CP3M) on FRED was discontinued in 1997. I would like to reconstruct this series in a reasonable fashion, so I can use it to analyze more recent events. I was ...
2
votes
2answers
83 views

How to find the best fitting GARCH model for a portfolio composed of 3 ETFs in R?

I am doing a project for my class Financial Time Series in which I am trying to forecast my portfolio log returns using a GARCH fit. I am having a bit of trouble determining the best way to fit this ...
2
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0answers
85 views

State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
2
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0answers
84 views

Derivation of variance of Zhou (1996) volatility estimator

Does anyone know how to derive the Variance of Bin Zhou's volatility estimator (Theorem 1) in 'High-Frequency Data and Volatility in Foreign-Exchange Rates' (1996) Zhou 1996 Any help would be ...
2
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0answers
166 views

Potential pitfalls in the use of correlation

Background: The red line is an index, which goes from 0 to 100, measuring uncertainty in the markets. The dark blue line is a price index, which has a lower bound at 0, and virtually no upper bound. ...
2
votes
1answer
299 views

Interpretation of cross-correlation matrix when one sample distribution is not normal

I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a ...
2
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0answers
224 views

Test for stationarity and make use of non-stationary points in financial market?

I have two questions to ask: What are the best methods to determine stationarity in a financial market (such as stocks) using MATLAB? What methods would you recommend to use in order to change from ...
2
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0answers
769 views

How to calculate the conditional variance of a time series?

I am reading a paper where the term conditional variance is mentioned, but I am not really sure what is meant by this and how this can be calculated: Fig. 2 shows the conditional variances of the ...
2
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0answers
62 views

Is there an appropriate sequence to tests during model diagnosis?

How should one order (sequence) the following tests? Stationarity test Johansen cointegration test Normality/Histogram test Autocorrelation test Heteroskedasticity test Multicollinearity test ...
2
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0answers
102 views

Difference between kappa and delta in mixed-effects model

(This question is a crosspost from Cross Validated) I have a following stochastic model describing evolution of a process (Y) in space and time. Ds and Dt are domain in space (2D with x and y axes) ...
2
votes
1answer
278 views

Average beta of index consitutents w.r.t. the index is 0.60

I have 1 year time series data of 300 constituents of the Australian All Ordinaries index (which is composed of 491 firms). The missing firms are mostly smaller firms. I run the market model $R_{it} ...
2
votes
1answer
617 views

a simpler test for normality given skewness, kurtosis and autocorrelation and size of time series

I typically do a JB (Jarque Bera) test and DW (Durbin Watson) tests for check for normality given skewness, kurtosis and autocorrelation of the data. However this requires a CHI distribution table ...
2
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0answers
258 views

What does T statistics of Information Coefficient indicate?

Hi I am looking for a clear explanation of T statistics concept. Especially in quantitative equity portfolio management context, what does T statistics of monthly Information Coefficient for one ...
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3answers
235 views

Handling Missing values in stocks returns when estimating the co variance matrix

What is the best way to handle missing values when stocks did not exist for the entire historical period?.
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3answers
70 views

Is there any way to easily estimate and forecast seasonal ARIMA-GARCH model in any software?

I use R to estimate a seasonal ARIMA(8,0,0)(5,0,1)[7] model for the seasonal differences of logs of daily electricity prices: ...
1
vote
3answers
1k 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 ...
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2answers
305 views

Optimizing Principal Component factor weightings over time

I was given the returns of a cross-asset class portfolio of ETFs and I conducted PCA to obtain factors on dates from T-n, T-3, T-2,..., T. What I would like to do is decompose the market moves from ...
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2answers
377 views

Transaction Data with Participant ID

For my master thesis, I need high-frequency data with the market participant ID or which identifies the trading parties, respectively. I don't need the entire orderbook but just the matched orders ...
1
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1answer
343 views

Why does $\hat{\epsilon}'\hat{\epsilon}$ of a factor model measure risk?

$\hat{\epsilon}'\hat{\epsilon}$ from the market model: $R_{it} - \hat{\alpha} - \hat{\beta}R_{mt} = \hat{\epsilon}$, or from a factor model such as the Fama-French 3 factor model, is often used in the ...
1
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1answer
91 views

detecting and measuring lead lag effect

Given two time series data. I remember there is one statistics that tells you one is the leading factor while the other is the lagging factor. However, i do not remember the exact details. correlation ...
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1answer
83 views

Estimate correlation of time series whose histories differ in length

Very often in quantitative analysis (e.g. calculating portfolio volatility) we have to analyze various time series - mostly returns - whose lenghts differ. Risk systems usually apply a one-factor ...