# Tagged Questions

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### PCA on term structure of interest rates

Interest rate time series seems to be non-stationary whenever test is performed But covariance or correlation matrix is derived from term structure time series which are non stationary and later PCA ...
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### Factor Model - Minimum Variance Portfolio [Complete Proof]

Can someone check my proof? I think there is something not quite right. I have found limited resources online for this as well so I think it might benefit others to get this on the internet. Assume ...
135 views

### Statistical arbitrage using eigen portfolios

I was trying to understand below paper https://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf Page 20 explains about "Entering a trade". I wan't to know clearly what it means to ...
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### Variance of “hedged” term structure portfolio increasing?

I'm attempting to use PCA to hedge a small fixed income portfolio. I start with one particular bond and chose the nearest other bond to hedge the 1st principle component. This decreases the portfolio ...
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### How to reduce fx currency pairs ? PCA or other tools?

I have 19 currency pairs like USD.AUD, USD.CAD, etc. Also 82 cross currency pairs like AUD.CAD, EUR.AUD,EUR.CAD etc. When I look to their graphs, most look similar, so I want to reduce number of pair ...
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### Looking for Research Paper on Creation of Currency Baskets

I came across a paper, not sure it originated from academia or a blog or such, that reported on applying principal components to build currency baskets from a set of individual currency pairs and to ...
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### Some clarifications on eigenvectors and eigenvalues from PCA

Could somebody tell me whether suggestions in bold true or not? Q # 1: http://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf ...
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### How to get permanently growing chart within PCA

I looked onto different questions and answers about application of PCA on this site and found this interesting article : ...
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### What is PCA and how does it relate to eigenvectors and eigenvalues?

What are the principal components? How they are calculated? What is their relationship with eigenvalues and eigenvectors? This is a lead-in question to explain PCA basics. EDIT: PCA is implemented ...
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### After PCA on original factors, how to tell which original factors are dominant?

When doing the PCA analysis, you end up with eigenvalues which are ordered by how much variance they explained for each eigenvector. Say, the eigenvectors since they are orthogonal, do not represent ...
228 views

### Non-negative matrix factorization for factor analysis of stocks

I stumbled over the term Non-negative matrix factorization in presentations such as Application of Machine Learning to Finance and this Big Data in Asset Management. The basic idea is to decompose a ...
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I have a return history for a universe of risky assets and I've run a principal component algorithm and obtained a loadings matrix (num_factors by num_assets) for the first 5 factors. I have a ...
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### PCA related Query

I am currently working on a project in grad school where I am using PCA Approach. I have 4 stocks. I used R to generate Eigen Values, Eigen vectors Eigen Values Number Value Diff ...
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### Can we model components in a set of multivariate multi-period time-series data?

There are N data sets in periods occurring weekly/monthly, across a 10-year historical timeline. In each period, five dates are observed (labelled a to e), where a denotes the day the period ...
231 views

### Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
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### Step-by-Step PCA algorithm (checking correctness without math packages)

I would appreciate if someone could correct me if i am wrong in my suggestion. I am using PCA to : find measure of cointegration between selected assets find the eigenvector and its portfolio with ...
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### Inferring signals in absence of sign of principal components (PCA)?

PCA seems to be very popular in dimension reduction applications and for extracting the top PCs which explain the data. One such application in futures is on the term structure to obtain the level, ...
295 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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### Are there any other standard rates term structure decomposition than PCA?

PCA is sometimes used to estimate components in the rates term structure. Are there any other standard method discussed in the literature or used in practice, what are their advantages and ...
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### Principle Component Analysis vs. Cholesky Decomposition for MonteCarlo

Let's assume we have a portfolio containing large number (~500) of risk factors. We want to simulate the portfolio dynamics. PCA based simulation would be faster as we can reduce the dimensionality. ...
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### Applicability of PCA to get historical volatilities to calibrate interest rates trees

My question in short is as follows: can I take main principal component of historical covariance matrix and use it as historical volatilities when fitting a binomial tree? Here's more detailed ...
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### How to use PCA for trading

Can anyone give me a few pointers of how to approach using PCA for trading? In particular, it seems to me, PCA is useful for selecting a subset of a portfolio of stocks(or other) rather than trading ...
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### How replicate data using PCA

I have a set of date covering petrol prices. My example has two columns where each row represents a sequential date. ...
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### PCA Variances and Principal Portfolio Variances

In Meucci's paper called "Managing Diversification" he mentions that: "Indeed, the eigenvalues A correspond to the variances of these uncorrelated portfolios" I tried to replicate it but found they ...
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### Interpretation of PCs

I have computed PC1 and PC2 wts on future contracts derived from cumulative log differences. How can I use them to get back the theoretical price of each contract using those 2 pcs? Thanks in ...
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### Why use market capitalization weighted index over PCA?

Why is it so popular to use market capitalization weighted indices instead of taking the first principle component that explains the most variation of the constituents? I haven't yet seen an academic ...
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### Estimating two normal random numbers with one equation

Subtitle: Estimating the correlation of the shocks driving two commodities in two multi-factor models I am fitting two 2-factor models to electricity and gas futures, respectively. In order to ...
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### How to make the final Interpretation of PCA?

I have question regarding final loading of data back to original variables. So for example: I have 10 variable from a,b,c....j using returns for last 300 days i got return matrix of 300 X 10. ...
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### Meta-view of different time-series similarity measures?

While I spend most of my StackExchange time on MathematicaSE, I'm in the business and follow the questions and answers on this site with great interest. Recently questions like the following (and ...
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I have a time series of data that is 300 days long. I compute PCA factor loadings on a moving window of 30 days. There are 7 stocks in the universe. Thus factors F1 through F7 are calculated on each ...
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### Why is the first principal component a proxy for the market portfolio, and what other proxies exist?

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...