Questions tagged [statistics]
The study of the collection, organization, analysis, and interpretation of data. Questions may deal with descriptive statistics, probability distributions, random variables, sampling, regression, density estimation, filtering, inference, estimation theory, or computational statistics.
432
questions
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31
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A term to compare 2 stocks based on simultaneous trending and ranging characteristics
There a 2 stocks called A and B. We take a look at the daily chart of both stocks over the last 1 year. On 90% of the days A and B both trended or at least one of A or B trended. On 10% of days both ...
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4
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129
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Оptimal strategy when throwing dice [closed]
Given a dice, you can throw it no more than three times, and you can stop at any time. How should you act so that on average you get as many as possible in the last throw?
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50
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Portfolio risk of correlated assets using Mahalanobis distance
I am trying to understand if there is an agreed methodology to measure the total risk in a portfolio of correlated assets.
I am taking a simple model of stock prices following geometric Brownian ...
- 207
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50
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Backtesting: choosing the "sample split" between in-sample and out-of-sample data
Aims:
Given approximately 11 years of historical time-series data, to determine how much of this data should be reserved for in-sample and ...
- 131
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votes
1
answer
81
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Test significance for information ratio
Suppose that we have an estimated Information Ratio $IR^*$ calculated from the relative returns between a portfolio and a benchmark.
I am looking for a way to quantify the uncertainty of this ...
- 1
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0
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41
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How to construct the probability of default (PD) with not much historical data (<1 year)?
If a financing company has a new funding program, is there a statistical method that can be used to construct a probability of default (PD) for IFRS 9 ECL calculation purposes? Considering that ...
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0
answers
40
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Effect size for information coefficient
The information coefficient is the correlation between a signal $g(t)$ and returns $r(t)$. I’m hoping to build some practical intuition on the information coefficient.
Similar to the notion of effect ...
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2
votes
0
answers
46
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Optimal Wallet Allocation for Algorithmic Trading under Random Alert Frequencies
I am an algorithmic day trader. I am trying to automate certain patterns on the stock markets. Suppose I have a model $M$ (with expected value $E$ and variance $V$) and a wallet with $X$ dollars in it....
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3
votes
1
answer
73
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Hypothesis Test Contradiction?
I have a question regarding hypothesis testing. I used the t-test (2-tailed) for these hypotheses:
Whether the (monthly) mean return of company A's stock is different from 0
Whether the (monthly) ...
- 31
3
votes
1
answer
178
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Effect of back-transforming forecasted mean of log returns to get forecasted mean of price
When trying to forecast time series, say forecasting the level of a stock index so we can forecast the future values of an option, it tends to be helpful to analyze the log returns versus the original ...
- 229
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81
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"fix" a sample covariance matrix which is not positive semidefinite by using daily returns instead of monthly
In the portfolio optimization problem at hand, one of the constraints is that the tracking error should not be greater than $\gamma$.
The constraint is therefore:
$(\textbf{x}-\textbf{w})^\mathrm{T}\...
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2
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0
answers
50
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Do resistance levels for financial securities prices exist? [duplicate]
I know there is a large controversy about whether or not technical trading rules are profitable and research results depend on asset classes, time frames, trading costs, risk-adjusted return ...
- 175
2
votes
1
answer
449
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Advances in financial machine learning (Marcos López de Prado): explanation of snippet 3.1
I have been reading AFML ( Marcos López de Prado
) and I am having trouble understanding snippet 3.1 which provides the following code:
...
- 63
2
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0
answers
59
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When the market is volatile, relatively fewer factors suffice for a productive stat -arb signal. Have you noticed it, and why would that be? [closed]
In volatile markets only a small number of factor are sufficient for factor based statistical arbitrage to work well. This is an empirical observation. Why would this be? Have others noticed it as ...
- 121
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89
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How to analyse the resilience of banks during financial crises using linear regression and other statistical methods?
I am a student in finance and have to work on a project for the semester.
I have to study the difference of resilience during financial crises between the 5 biggest US banks and the 5 biggest Canadian ...
- 11
3
votes
0
answers
126
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Roll Critique - CAPM and mean variance tautology?
Wikipedia introduces the Roll Critique mean-variance tautology:
Any mean-variance efficient portfolio $R_p$ satisfies the CAPM equation exactly:
$$
E(R_i) = R_f + \beta_{ip}[E(R_p) - R_f]
$$
A ...
- 131
1
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0
answers
49
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Testing predictability of a proposed predictor in case of multiple returns
Say I have a T daily observations for the last ten years on a new predictor $x_t$ which I think is a predictor of the expected weekly return on the stock market, $r_{t,t+5} = r_{t+1}+...+r_{t+5}$, ...
- 11
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0
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23
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Empirical estimation of the rate parameter in exponential distribution of time arrivals
I am recording the execution time of aggregated trades on the BTCUSDT market on Binance. The websocket server delivers messages of the following form
{"e":"aggTrade","E":...
- 213
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0
answers
133
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Intraday tick volatility between a time interval
I would like to calculate intraday tick volatility between a time interval A to B.
E.g. If I have the quote and trade ticks for an instrument between 2023-02-17 10:00:02 to 2023-02-17 14:30:00, would ...
- 93
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0
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24
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sampling distribution function
from here https://mathworld.wolfram.com/StandardDeviationDistribution.html,
can someone please explain where that distribution function came from? Many thanks
- 121
3
votes
1
answer
110
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Compute monthly realized variance for Fama-French factor
I need to compute monthly realized variance from daily data for Fama-French factors. Knowing that Fama-French factors is the difference of return between different type of stocks, for example SMB ...
- 43
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0
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59
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Most famous research papers to get started in quant finance [duplicate]
I have a strong background in finance and I know how to code, but I am lacking the statistical modelling part. I have started courses in mathematics and statistics. However, it is turning out very ...
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3
votes
3
answers
355
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How to identify daily returns as an unusual daily return given a dataset
I am currently calculating daily returns of a stock with the following formula:
$$R_t = \frac{P_t - P_{t-1}}{P_{t-1}}$$
However, once I have the data, I am unable to establish a range to classify the ...
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1
vote
1
answer
356
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Compute monthly realized variance from daily data
I am confused about the correct formula to compute monthly realized variance from daily data. What is the first sigma in the picture: sum or average? I mean, after subtracting each observation from ...
- 43
2
votes
0
answers
69
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Idiosyncratic risk (t statistic)
I am working on idiosyncratic volatility analysis and I would like to control for size characteristics following the method used in the paper "The Cross-Section of Volatility and Expected Returns&...
- 85
2
votes
1
answer
291
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What program to use for reverse MIDAS?
I know EViews is used for mixed-data sampling (MIDAS). Can someone pls help me identify a program I can use for reverse MIDAS? Thank you.
- 21
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0
answers
23
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Machine learning on NASDAQ [duplicate]
I want to perform an ML analysis on NASDAQ, based on historical fundamentals.
Suppose I want to take a temporal window of 10 year and quarterly data.
I have a question:
I suppose I should know the ...
- 1
5
votes
2
answers
390
views
Cointegration between crypto markets
I'm having an hard time understanding how cointegration works. Basically i'm trying to find cointegrated pairs in the crypto market, so i do the following:
Get OHLC data for the two markets (i'm ...
- 51
0
votes
1
answer
239
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How to implement rolling granger causality
I am investigating two time series where the first is the daily closing stock price changes and the other is the daily changes in the PCE index.
I want to investigate how much the PCE index explains ...
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0
votes
2
answers
92
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Correlation with Differ Units of Measurement [closed]
I was wondering how to accurately get the correlation between a variable of percent change return and a variable of dollar change or basis points. Should I standardize both variables or will that lose ...
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0
answers
63
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Reasons for negative autocorrelation of forward prices
I am working on each trade day's forward prices of gasoline. I noticed that the autocorrelation at lag 6 is significantly negative. I know how to interpret negative autocorrelation in a statistical ...
- 1
0
votes
2
answers
297
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How can I measure returns such that the average is useful?
If I measure daily returns by simple percent change, a -50% day then a +50% day (or vice versa) results in a true -25% total change, but the average makes it look like you would expect a total 0% ...
- 11
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votes
0
answers
36
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Retail vs institutional percentage estimation in equity futures market (CME)
I am trying to find the most/least "popular with retail futures traders" instrument based on public data. I managed to estimate retail/institutional proportions by aggregating OI data from ...
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2
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0
answers
310
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Using the Fama-French 5 factor model in Panel Data
I have a question regarding the use of the FF5 Factors in an industry-fixed effects model. In order to clearify my question I'll post an example of my dataset
Note that this is just an example, the ...
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0
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140
views
What is the Kurtosis of Returns in Geometric Brownian Motion?
Suppose that $dS_t=S_t(\mu\mathop{dt}+\sigma\mathop{dW_t})$ which has solution
$$S_t=S_0\exp\left(t\left(\mu+\frac{\sigma^2}{2}\right)+\sigma W_t\right),$$
such that $W_t$ is a Wiener process, $\mu$ ...
- 128
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votes
1
answer
561
views
Principal component analysis on a yield curve
When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4?
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53
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Average probability of varying input data
New to the quant finance exchange. I am stuck with a question maybe someone could help me.
In the table below I have calculated if price is up/down w.r.t to the open shown in the 2nd column with ...
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1
vote
0
answers
125
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Normalized statistical risk/reward measures to compare different quant trading strategy's returns, eg for backtesting
Want to select a metric or metrics to compare returns of different investment strategies, for quantitative backtesting, strategy selection, and forward measurement.
Been reading different approaches ...
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3
votes
1
answer
222
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Interpreting the average correlation figure in Pozzi et al. (2013) paper
Has anyone read the paper "Spread of risk across financial markets:better to invest in the peripheries" by F. Pozzi, T. Di Matteo & T. Aste? If so, how do you interpret equation (1) in ...
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1
answer
142
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What are the most common methods to model fat tails in the changes of asset prices?
I was wondering what the most common, or most popular, ways - in both academia, and industry - there were to model the fat tails of volatility in asset prices changes.
I am presuming a basic Brownian ...
- 103
1
vote
1
answer
210
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Statistical metric to measure how well does the volatility surface fit the market
Suppose that I have a model for implied volatility surface and want to figure out required recalibration frequency based on historical quotes. Since I have a large range of strikes and tenors over a ...
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2
answers
253
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Is it safe to assume inflation rate and treasury yields are stationary?
I have YoY percent change in CPI and the nominal 10 year Treasury yield.
I want to run some correlation analysis between them but worry they are not stationary. I ran a DF test and found that, ...
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0
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186
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how to derive t-statistic for alpha (Eq. 15.29) in "quantitative equity portfolio management"?
I am reading "quantitative equity portfolio management: an active approach to portfolio construction and management" by Ludwig B. Chincarini, Daehwan Kim, and am confused by this derivation ...
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123
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Why do Monte-Carlo methods converge quadratically?
I'm reading Sutton's Reinforcemant Learning: An Introduction, and here's a part from page 93 of this book:
In this case each return is an independent, identically distributed estimate of $v_\pi(s)$ ...
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1
vote
1
answer
447
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Shrinkage of the Sample Covariance matrix, theory
is there any theory behind the covariance matrix shrinkage paper, why it works?
I am talking about this stats exchange thread
- 143
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0
answers
50
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Which distribution has higher VaR?
Let say I have 2 distributions with cdf $F_1$ and $F_2$. And I know that $F_1 \leq F_2$. With this information I know that $F_1$ has bigger lower tail than $F_2$ but I don't think this right away ...
2
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0
answers
176
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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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3
votes
2
answers
653
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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1
answer
106
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Compare errors in estimating a probability
Let $X_t$ be a geometric Brownian motion: $dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t$ with $W_t$ a standard Brownian motion.
Given the intervals $[t_{j-1}, t_{j}]$ for $j\in {1,...,U,...,N}$, let $M_j$ ...
- 125
1
vote
1
answer
343
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How to conduct statistical test to see if certain factors impact trading streategy
Since the seminal paper by Fama and French(1993) that uses size, market, and value factors to explain extra market returns on the equity market, people have conducted tons of research on equity factor ...
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