Questions tagged [estimation]

The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.

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To estimate the parameters when only the characteristic function is known to us

Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data. To obtain VGSA, as explained in Carr et al. [2001], we take ...
Starlord22's user avatar
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In which context do hedge funds use the Gauss Markov Theorem?

Hedge Funds really like asking questions about linear regression during interviews. Especially about the properties of the OLS. But I don't understand in which context this is used. For example the ...
confucius_is_confused's user avatar
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Estimate of 90-day volatility using GARCH when I have minute-by-minute data

I have minute-by-minute data and would like to use GARCH to produce an estimate for 90-day ahead volatility. I'm using the arch_model library in Python which has a <...
Julie Taylor's user avatar
2 votes
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What quantities (means, betas) must be constant over time for the GRS test to be valid?

I am interested in testing the CAPM using the GRS test. Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test amounts to ...
Richard Hardy's user avatar
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Resource recommendations: Levy process estimation using programming languages

Perhaps this type of question is not very suitable for this forum, but I'll try to make my question a little useful. I'm studying stochastic processes, more precisely, Levy processes. A Levy process $...
André Goulart's user avatar
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Stochastic volatility estimation in R

Can anyone help me with the stochvol package in R? I estimated the volatilities using this package but I am not being able to understand how to download the ...
nusratecon's user avatar
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1 answer
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R resources for GMM estimation and testing of multifactor asset pricing models

Has anyone seen R script for GMM estimation and testing of asset pricing models such as Fama-French 3-factor or similar? Ideally, I would like to have R scripts corresponding to Cochrane "Asset ...
Richard Hardy's user avatar
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GMM estimation of the CAPM allowing for time-varying expectation of market's excess return

With time-constant expected value of market's excess return, we can estimate the CAPM using GMM as follows. Equation $(12.23)$ in Cochrane "Asset Pricing" (2005) section 12.2 (p. 241) says ...
Richard Hardy's user avatar
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How to set up a panel data model for estimating the CAPM?

In this question, I asked whether it is better to use clustered or GMM-based standard errors for estimating and testing asset pricing models such as the CAPM. However, I then realized that I am not ...
Richard Hardy's user avatar
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Estimate Open, High and Low prices from bid, ask and close prices

I know it's possible to efficiently estimate bid/ask spreads from OHLC prices and there are several methods to do so. However I have a data source that contains only bids, asks and close prices, no ...
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Estimation of the Vech HAR model (Multivariate HAR)

I am trying to use the Vech-HAR (the mulitvariate HAR) model in order to forecast some covariances. I have been looking into the model proposed by Chiriac Modelling and forecasting multivariate ...
Sim's user avatar
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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":...
apt45's user avatar
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Incorporating idiosyncratic risk as a pricing factor with GMM

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing an augmented CAPM or a multifactor model with an additional factor: the ...
Richard Hardy's user avatar
1 vote
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275 views

Definition and estimation of $\beta$: raw or excess returns?

The CAPM is a single-period model that says $$ \mathbb{E}(R^*_i)=\beta\mathbb{E}(R^*_m) $$ where $R^*_i:=R_i-r_f$ is an asset's excess return, $R^*_i:=R_m-r_f$ is the market's excess return and $\beta:...
Richard Hardy's user avatar
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Testing the CAPM: does GRS account for errors in variables (measurement error)?

Suppose we are interested in testing the CAPM using the GRS test. Consider $N$ assets observed for $T$ time periods. Using the notation of Cochrane "Asset Pricing" (2005), the GRS test ...
Richard Hardy's user avatar
2 votes
2 answers
172 views

GMM estimation of the CAPM: why not include sample mean of the market excess return as a moment?

I am trying to wrap my head around GMM estimation of a single factor model such as the CAPM. I started by asking How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)? ...
Richard Hardy's user avatar
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How come the cross-sectional CAPM equation produces $N$ moment conditions (not $1$)?

Reading Cochrane "Asset Pricing" (2005) section 12.2 (p. 241), I got lost in the derivation of the GMM estimator for the single-factor model. Equation $(12.23)$ says the moments are $$ g_T(b)...
Richard Hardy's user avatar
6 votes
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Clustered vs. GMM-based standard errors: which ones to use in asset pricing?

Consider estimating an asset pricing model such as the CAPM or a multifactor model using monthly data. Petersen (2009) section "Asset pricing application" suggests use of standard errors ...
Richard Hardy's user avatar
1 vote
2 answers
121 views

Imposing diagonality of error covariance matrix when the CAPM holds

Assuming that the CAPM holds, the total risk of an asset can be partitioned into systematic risk (associated with the market factor) and idiosyncratic risk. Idiosyncratic risk is asset specific. Does ...
Richard Hardy's user avatar
2 votes
1 answer
141 views

Why estimate the (known) market return in the cross-sectional regression of Fama-MacBeth?

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing the CAPM. Using Fama-MacBeth style analysis, we first estimate $N$ time ...
Richard Hardy's user avatar
4 votes
1 answer
239 views

Incorporating idiosyncratic risk as a pricing factor Fama-MacBeth style

Suppose we are given a dataset with $T$ time periods and $N$ assets or portfolios. We are interested in estimating and testing the CAPM or a multifactor model. Take the CAPM: $$ r^*_{i,t}=\alpha_i+\...
Richard Hardy's user avatar
2 votes
1 answer
111 views

Filtering SDE for Heston Volatility

Consider a GBM model with Heston volatility: $$dS_t = \mu S_t dt + \sqrt{V_t} S_t dB_t^1$$ $$dV_t = \kappa(\theta-V_t)dt+\xi \sqrt{V_t}dB_t^2,$$ where $(B_t^1, B_t^2)$ is a correlated BM. Let $$\...
Nap D. Lover's user avatar
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Estimating Zero Coupon Curve using only Fixed-Coupon bonds available

Today I have been struggling with something that someone here for sure has already encountered. I have a corporate issuer with a set of fixed coupon bonds (maturities between 1.5 to 20+ Years, luckily ...
Monchinga's user avatar
1 vote
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Estimating the relationship between short-term intretes rates and 10Y bond yields

On the 16th of March 2020, the Polish Central Bank announced its first-ever round of Quantitative Easing. I am conducting an event study on how this announcement impacted the term structure. The main ...
borninthenorth's user avatar
1 vote
2 answers
145 views

Estimating historical volatility from inconsistent time intervals

Given historical asset prices at consistent time intervals, one can estimate annual volatility as: SampleStDev(log(Si/Si-1)) / sqrt(interval) What's the correct way to do this when the time intervals ...
Kalev Maricq's user avatar
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1 answer
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Estimate market positioning from flow data

I have a set of time series data from a bank that is transaction data from all its clients on a particular currency. From that data, I attempt to estimate the current "position" of all ...
Felton Wang's user avatar
1 vote
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62 views

2-step system-GMM for static panel models?

Could we use the 2-step system generalized method of moment (GMM) for static regression models? As I know, 2-step system GMM is designed for dynamic panel data models but I see many papers use it for ...
Tina Ha Dinh's user avatar
1 vote
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535 views

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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A Bayesian-Stein based expected return estimator by J.P. Morgan

Please consider the following estimator for the expected returns specified in the paper "Improving on risk parity: Hedging forecast uncertainty" by Peter Rappoport, J.P. Morgan, October 2012....
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Correct terminology - estimate or model?

I am doing some academic work and I'd like to summarise the picture around volatility models. As such, I'd like to refer to several ways of estimating volatility and I'd like to use proper terminology....
s5s's user avatar
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2 answers
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Calibrating OU parameters using AR(1)

I have a mean reverting time series and want to find the Ornstein-Uhlenbeck (OU) parameters of it. I researched the internet and found that we can calibrate the model as a simple AR(1) process, $$\...
shananims's user avatar
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2 answers
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Estimating the variance of returns with aggregated data

Say I have an asset return time series: Jan2020: -5% Feb2020: +5% Mar2020: -5% Apr2020: +5% May2020: -5% Jun2020: +5% Q3 2020: +20% Oct2020: +5 Nov2020: -5 Dec2020: +5 Note that 3 months of data is an ...
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How does yahoo calculate Growth Estimates

Does anyone know how yahoo calculates Growth Estimates for the Next 5 Years (per annum)? For example, I can see 12.64% for AAPL as reporetd in Yahoo finance in https://finance.yahoo.com/quote/AAPL/...
Stat's user avatar
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Mean estimate in portfolio optimization (Markowitz) [duplicate]

The Markowitz mean-variance portfolio optimization problem is to find the optimal allocation, $w_{optimal}$ by solving: \begin{equation} w = \mathrm{argmax} \ \mu_{t}^Tw - \frac{\gamma}{2}w^{T}\...
MathStat2718's user avatar
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Entropy-implied volatility requires itself to be calculated?

\begin{align} H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\ &= \frac{1}{2} \ln (2\pi e \sigma^2) \end{align} is the analytical solution for the entropy of a Gaussian random variable, ...
develarist's user avatar
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2 votes
0 answers
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Estimating constant and local volatility based on passage times

Consider a Brownian motion B_t with constant instantaneous volatility σ and zero drift where ...
HJA24's user avatar
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1 vote
3 answers
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Do portfolio mean and portfolio variance have probability distributions?

If $X$ is a $T\times N$ matrix of multivariate asset returns, and $w$ is some optimal portfolio weight vector, then the portfolio return series is $r_p = X w \in\mathbb{R}^{T}$. This return series ...
develarist's user avatar
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1 vote
1 answer
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A simple question about VaR estimation

"A 99% VaR using 1,000 (simulation) replications should be expected to have only 10 observations in the left tail, which is not a large number. The VaR estimate is derived from the 10th and 11th ...
techie11's user avatar
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2 votes
1 answer
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Question on the use of a limit in a proof

I ran into a step in an argument that I can't quite figure out. It's basically how they use a limit that I don't seem to understand. The context is local-to-unity asymptotics in vector autoregressions,...
Stéphane's user avatar
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1 vote
1 answer
498 views

Do EWMA weights remove autocorrelation in asset returns?

I know that the exponentially weighted moving average (EWMA) volatility estimator drapes a decaying weight function over historical returns in order to weight the past according to the decay of their ...
develarist's user avatar
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11 votes
9 answers
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Why is asset volatility easier to estimate than the asset mean if it contains the mean?

It is well known that the variance of asset returns, $\sigma^2$ (whose square root is volatility), is easier to estimate than the asset mean $\mu$ (also known as expected return) because the mean of ...
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2 answers
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Do the weights of the exponentially weighted moving average (EWMA) have to sum to 1?

I am currently trying to calculate a volatility by using the EWMA model because it is said to yield better results than just using an equal weighted calculation approach. However I am a bit confused ...
Sanoj's user avatar
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Can you approximate stochastic volatility processes using GARCH processes?

Let me specific. Suppose that you have the following process: \begin{align} z_t &= \sigma_t \epsilon_t \\ \sigma_t &= \sigma \exp \left( \frac{v_t}{2} \right) \end{align} where $v_t$...
Stéphane's user avatar
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2 votes
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Correcting high AR(1) coefficients in dynamic Gordon model

I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis. However after receiving some feedback there is one last issue I want to resolve. I'm using ...
Niek de Meijier's user avatar
0 votes
1 answer
529 views

Implementing Fama-MacBeth cross sectional regression

I have built a Fama and French three factors model (market excess return, small-minus-big, high-minus-low) and estimated its betas through a time series regression (code in R, but any other language ...
Vitomir's user avatar
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4 votes
1 answer
240 views

Change of measure

I am looking at the derivation of the Hill estimator. It is $ \bar{F}(x) = 1 - F(x)$ the right tail of the distribution. In the derivation they use the equation $$ \frac{1}{\bar{F}(u)}\int\limits_u^\...
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Are asset return means difficult to predict because they have no lower bound?

In finance, it is widely known that the volatility of asset returns ($\sigma$) are easier to predict than the expected value of asset returns ($\mu$) , otherwise known as the average return or mean. ...
develarist's user avatar
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3 votes
0 answers
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Are intraday volatility estimators useful for close-to-close predictions

I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
Volwiz's user avatar
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2 votes
2 answers
234 views

How to predict realised variance?

I am trying to predict the realised daily close to close variance of an equity index. I checked the literature on volatility forecasting and tried a bunch of things on a dataset for the S&P 500....
Volwiz's user avatar
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realized correlation estimation

I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: On covariance estimation of non-synchronously observed diffusion processes, 2005) and there's something ...
apocalypsis's user avatar