Questions tagged [time-series]

A temporal sequence of events measured at discrete points in time.

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15 views

Computing the average deviation range in a mean reverting series

Given a mean reverting time series, what's the appropriate measure to use to compute the range it deviates by before reversion? Assuming normal distribution, taking standard deviations of the actual ...
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41 views

Probability of a certain financial instruments movement

I want to calculate the probability of a certain financial instrument moving above or below a certain threshold within a certain time frame. Let's say up 0.5 % within the next 4 hours. If we assume ...
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Looking for a measure of a simple Trend and Strength Indicator

I'm not literally a Quant but rather an analyst working in Process Control and I have a problem that I think could be solved with the Financial tools. Basically I have a matric called DPM (Defect Per ...
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How to generate normalized factor scores for beta exposure

I'm working on building a time series momentum model (TSMOM) based on price alone for currency pairs. I'm implementing a paper that produces a buy/sell signal based on geometric brownian motion and a ...
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74 views

Moving Average Window Size Determination

Is there a "correct" way of determining a moving average window/smoothing parameter (or at least a starting guess for a financial time-series? I understand of course that in some sense, ...
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1answer
54 views

Understanding Volume Bars Threshold

I have been reading Advances in Financial Machine Learning by Marcos López de Prado and came across different Bar types, and simulating Volume Bars from execution data myself. My understanding of ...
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1answer
30 views

Continuous futures data roll adjustment

When I construct continuous futures data (Wheat futures for example), I get different results than barchart or tradingview. Examples below. The 1st image is my adjusted continuous data and the 2nd ...
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25 views

[PYTHON - Create a For-loop for multiple regressions within the same/or different dataframe/s (Funds returns with fama french)

hopefully somebody can help me out, this is my first question on here. I have a dataframe with dates (Index) as the Y axis and the X axis (columns) hold all the dependent variables (target variables) ...
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Fitting ARIMA + GARCH in R

I'm forecasting Electricity consumption Data. I have data for one year , so for every 15 minutes there is an observation. My data contains seasonality and I don't know how to fit SARIMA + GARCH into R,...
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233 views

How can momentum trading strategies work if returns are not serially correlated?

Returns are demonstrably not serially correlated in most financial time series (Day 1 returns are uncorrelated to Day 2 returns etc.) . Since this is the case, how can momentum trading strategies work?...
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Charting Annual Volatility From Start Date In a Line Plot

I'm pretty new to python/data viz and this is my first time asking a question on here but I have a df with monthly price data back to 2016 for 6 different instruments. I just want to be able to ...
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114 views

I am getting an $\alpha=0$ in the GARCH(1,1) model. Is this normal and how must I interpret it?

I am running a GARCH(1,1) on return data. For some data sets, I am getting an $\alpha=0$ and a $\beta$ of 0.999. Is this normal? If so how should I interpret it? Here is my code, here j are daily ...
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169 views

Understanding out-of-sample performance metrics for Realized Volatility

I fitted several models on a realized volatility process and then proceeded to obtain out-of-sample results. I'm struggling to interpret these results apart from to tell model A seems better than ...
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Bitcoin data (minutes time frame)?

Where can I find a correct data of BTC/USD with a minute time frame? I've downloaded a minutes data from this site I've compared (with the original one from the exchange Binance) the last day (from ...
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1answer
138 views

Why is $Z_t$ uncorrelated with $X_{t-1}$ in $X_t=\theta X_{t-1}+Z_t$?

In a solution to the problem below, the teaching assistant solves it by calculating $\mathbb{E}[X_t^2]$ and ends up with also having to calculate $\mathbb{E}[X_{t-1}Z_t]$ after expanding the square. ...
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How to annualize kurtosis of returns (in simple terms)?

I'm confused by this post on how to annualize kurtosis. I don't understand how to apply it to annualize the kurtosis for my data. In other words, if I evaluated the kurtosis of, say, monthly returns (...
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Which Times Series Database framework for Python is best for portfolio optimization project?

I am starting to build a portfolio optimization algorithm in Python and want to structure a database to manipulate financial data. Although I have Python experience, I have never used SQL or such ...
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What is a cumulative return series?

I guess this is pretty easy but I cannot find a definition anywhere. I am trying to reproduce a paper and they say they use a cumulative return series at some point. Does anyone know exactly what this ...
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What do I need the Error correction model for in the two step Engle Granger approach (bivariate Cointegration)

could someone kindly explain what I need the ECM for in a bivariate Cointegration test? I am currently trying to reproduce the results of Rad et al. (2015): "The profitability of pairs trading ...
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35 views

How to calculate price and volume samples of a multi-product series?

I am reading Marcos de Prado's Advances in Financial Machine Learning. In a section titled "the ETF Trick", he explains how to calculate periodic price and volume samples for a basket of ...
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42 views

Converting timeframe of a time series

So I've encountered a problem - I have a lot of 1 min data, but my strategy works better on longer timeframes and backtrader has some problems with backtesting on 1 mln rows. I want to convert it to ...
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222 views

Trading a Bouncy Stock

I came across the following question and am trying to understand it better. I was hoping you could share your intuitions. For a given stock, you are certain that for the next 100 days, it will move ...
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in time series analysis or finance people use log return for inference but returns can take negative value [closed]

in time series analysis or finance people use log return for inference but returns can take negative value. but log cant take negative values. so why we use it when log is not defined on most of ...
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Proof of the fact that roots lie outside the unit circle guarantee stationarity of the time series

For an AR(p) process $$\begin{align} y_t &= \mu + \phi_1 y_{t-1} + \phi_2 y_{t-2} + \cdots + \phi_p y_{t-p} + \epsilon_t \\[4ex] &y_t (1 - \phi_1 L - \phi_2 L^2 - \cdots - \phi_p L^p) =\mu + \...
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1answer
85 views

Prediciting outperformance - choice of statistical design?

I want to predict relative outperformance between a stock and an associated benchmark index using statistical time-series models (e.g. ARIMA) and some exogenous variables (day of the week, corporate ...
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152 views

GARCH(1,1) parameter estimation optimization method

In estimating a GARCH(1,1) model, $$\sigma_{t+1}^2 = \omega+\alpha \epsilon_t^2+\beta\sigma_t^2$$ Usually the parameter tuple $(\omega,\alpha,\beta)$ is estimated by the quasi-maximal likelihood. ...
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1answer
72 views

GARCH parameter estimation by linear regression?

In estimating a GARCH(1,1) model, $$\sigma_{t+1}^2 = \omega+\alpha \epsilon_t^2+\beta\sigma_t^2$$ Usually the parameter tuple $(\omega,\alpha,\beta)$ is estimated by the quasi-maximal likelihood$. Can ...
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52 views

Compare portfolio returns across time dimension

I've designed a trading strategy and would like to understand whether the return profile for it differs for the trades implemented before and after the Covid pandemic. Specifically I would like to ...
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1answer
117 views

Quantative way to evaluate divergence and convergence between time series

Given, for example, two time series asset price and its associated relative strength index (RSI), what would be the quant way to evaluate convergence or divergence on a rolling-window basis? I'm ...
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19 views

Calculate series of cashflows based on a fixed value for their difference in net present value

I have two time series of cashflows, one for renting a building and one for buying it. Normally I calculate the net present value for both cashflows and then calculate their difference. I do this for ...
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158 views

Current research in price prediction

I am returning to studying the markets after ten years spent in banking. I would like to ask for directions, what approaches to price prediction are currently used - I want to catch up quickly. Papers ...
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186 views

Markov Switching Vector Autoregressive (MSVAR) and Markov Switching Dynamic Stochastic General Equilibrium (MSDSGE) Models

I want to reproduce the results of Bianchi et al (2017) Escaping the Great Recession using R and/or Python. Authors in the ...
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1answer
116 views

Simple Blockbootstrap instead of CircularBlockBootstrap

I am currently trying to Block-Bootstrap my Stock-return data in Python. I am doing that to generate synthetic data. I came across the CircularBlockBootstrap but found in a few discussions here that ...
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2answers
171 views

Trouble Calibrating a Vasicek Model

I have simulated some data according to a Vasicek process and I am then trying to apply ordinary least squares (OLS) regression analysis to see how accurate the estimated model parameters are from the ...
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1answer
49 views

Find best linear predictor of $X_2$ given $1, X_1$

I'm having a problem calculating the best linear predictor of a time series. I'm using the book Brockwell-Davis 2016 - Introduction to Time Series and Forecasts. First let me write down one notational ...
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1answer
323 views

Realized Variance (realized volatility)

I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
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25 views

SVAR, seasonality adjustment and impulse response functions

My question might be slightly dumb, however I could not find out which choice would be better. I am trying to construct a SVAR model including the french inflation rate, the unemployment rate and the ...
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1answer
144 views

Are return time series ergodic?

It seems intuitive to me that return time series would be ergodic. Is there a test statistic that I can use to check this? Would this be affected by sampling rate? One way I can think of checking ...
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163 views

Statistical methodology for proving the stability in time of asset allocation weights

I am comparing the set of weights obtained by the classical Markowitz allocation process with those of another asset allocation technique I have devised. Markowitz's weights are unstable, as the ...
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28 views

FamaFrench, FamaMacBeth or Panel regression?

I hope my question is not extremely trivial. I want to analyse the performance of mutual funds using the Fama-French model. My dependent variable is the return of mutual funds (varying over time and ...
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1answer
48 views

Show that $\text{Cov}[X_r,X_s]=\text{Cov}[X_{r+h},X_{s+h}]$ for $X_t=a+bZ_t+cZ_{t-2}.$

Problem: Let $\{Zt\}$ be a sequence of independent normal random variables, each with mean $0$ and variance $\sigma^2$, and let $a$, $b$, and $c$ be constants. Is $X_t=a+bZ_t+cZ_{t-2}$ a (weakly) ...
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108 views

Bad plots in python, good plots in excel

I am wondering if you could solve the mystery about why matplotlib / seaborn give me a line plot of the IBM stock price, which is terrible as you can see below, with some vertical lines that are of ...
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139 views

Show that $Y_t$ and $Y_{t+h}$ are independent if $X_t$ is Gaussian

If $Y_t=\sum_{i=0}^qa_iX_{t-i}$ where $X_{t-i}$ is Gaussian with mean $\mu$ and variance $\sigma^2$, how do I show that $Y_t$ and $Y_{t+h}$ are independent (for $|h|>q$) using the joint pdf. I know ...
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152 views

Question about slides in lecture note: What if we can't assume $\mu=0?$

The question popped up when I was reading these lecture notes online. Consider the MA$(1)$ process given by $X_t=W_t+bW_{t-1}$ where $W_t$ is white noise distributed with constant variance $\sigma_W^2....
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77 views

Estimating distribution of rate of return

Let $f[t]$ be the price of a stock at time $t$. We can calculate the rolling rate of return of the stock in a window of length $n$ by computing: $$r[t] = \frac{f[t] - f[t-n]}{f[t-n]}$$ $r[t]$ is ...
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53 views

CAPM: Testing for alphas jointly equal to zero

For my project, I need to assess if a certain factor X leads to a CAPM-Anomaly. First, I sorted the monthly stock return (sample size: 500+ observations) according to the X factor in 10 decile ...
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1answer
87 views

Show that $\text{Cov}[Z_t,Z_{t+h}]=\text{Cov}[Z_s,Z_{s+h}].$

Problem: If $X\sim\text{WN}(\mu,\sigma^2).$ Let then $Z$ be the process defined by \begin{equation} Z_t=\sum_{i=0}^na_iX_{t-i} \end{equation} for some coefficients $a_1,...,a_n\in\mathbb{R}$ with ...
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59 views

Is the mean of a stationary timeseries the same everywhere?

Say for example I have the white noise process $Y_t\sim\text{WN}(\mu,\sigma^2)$. Is it true that $\mathbb{E}[Y_t]=\mathbb{E}[Y_{t-h}]$, where $h\in\mathbb{N}?$
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48 views

How to compare or prove economic/statistical similarities between two models with differing independent and dependent variables?

I have two datasets: The relationship between Bitcoin prices and other cryptocurrencies. The relationship between EUR prices and other currencies. What would be the most appropriate way to prove ...
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58 views

Calculation of Expected Shortfall using IMA Approach ( FRTB)

I am trying to calculate the Expected shortfall of a FX portfolio through IMA Approach of FRTB in excel . I have used several combinations in excel to get the liquidity horizons and then calculate the ...

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