This is the third and final post in the mini-series on Autoregressive Moving Average (ARMA) models for time series analysis. We've introduced Autoregressive models and Moving Average models in the two previous articles. Now it is time to combine them to produce a more sophisticated model.

Large institutions deal with immense amounts of currencies which enter and leave their accounts on a daily bases. Furthermore they have their own funds that it has to efficiently allocate so as to maximize their return on investment but also wish to hedge against adverse events. With a certain

Michael Himmel is a Founding Partner, Portfolio Manager and Director of AI Research for Essex Asset Management. He has been actively trading and designing systems since the 1980s, managing the No.1 Global Macro Hedge fund in the world in 1999. He now uses large doses of AI and Machine Learning in

The best quant mashup links for the week ending Saturday, 09/05 as voted by our readers: Announcing the Release of My New Book [Price Action Lab] VIX Trading Strategies in August [Volatility Made Simple] Systems building – Checks and balances [Investment Idiocy] Counter-Intuitive Facts About

Acceleration Effect and Gamma Factor in Asset Pricing (improved Momentum)

Almost all calculations in finance involve using log returns rather than % returns. There are a number of reasons why log returns are preferred. Estimating beta doesn’t seem like a special case. But when you go through the math, something doesn’t quite add up.

Benford's Law states that in many naturally occurring groups of numbers, the small digits are seen disproportionately often. This is often applied to the leading digits of data but it is more general than that. This was first noticed by the astronomer Simon Newcomb (who also should be famous

Light is the most precious resource to a photographer, everything you can do with your camera is budgeted by the amount of light available. Financial analysis is similarly constrained by the amount of data available. So more available data is always good. With Big 'O' Sharpe you can

I’ve replicated the following academic paper from my favourite journal; • Title: Nonlinear support vector machines can systematically identify stocks with high and low future returns • Authors: Ramon Huerta, Fernando Corbacho, and Charles Elkan • Journal: Algorithmic Finance (2013) 45-58 45,

This post will begin to apply a hypothesis-driven development framework (that is, the framework written by Brian Peterson on how to do strategy construction correctly, found here) to a strategy I’ve come across on SeekingAlpha. Namely, Cliff Smith posted about a conservative bond rotation

I have shown the study below a several times in the past, but not for a while. It examines the recent performance in the overnight futures market on nights the Employment Report has been released since the summer of 2012. The Employment Report is released at 8:30 AM Eastern (normally the 1st Friday

August 2015: Trend Following UP +2.36% — YTD: +8.94% The Summer bounce seen last month continued in August, with a positive monthly return pushing the YTD performance further up in the black. The last ten days of the month saw two strong days taking the index close to a +10% return, followed by

It seems reasonable that institutional trades could influence stock returns. Any large trades will move prices. In fact, a fairly common trading strategy is to try to detect the presence of large institutional trades in order to piggy-back on the flow. Also, large institutions have access to a lot

#14 - Momentum Effect in Stocks #25 - Small Capitalization Stocks Premium Anomaly Authors: Schmidt, Von Arx, Schrimpf, Wagner, Ziegler Title: Size and Momentum Profitability in International Stock Markets Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2642185 Abstract: We study the link

Over the last six blog posts we looked at the backtest results for over 13,700 options strangles sold on the Russell 2000 Index (RUT). Eight different exit approaches were tested on these strangles, including: Strangle (100:50) - exit if the trade has a loss of 100% of its initial credit OR if the

Driverless cars are, apparently, very close to commercial reality. I don't know about you but there is something pretty scary about a computer being completely in control of a complex process, which could have catastrophic consequences if it went wrong. Ah it was nothing. You should have seen

Some assert that once a strategy is “discovered” it can’t work anymore. Others, often implicitly, assume the future will look as wonderful as the past. Perhaps not surprisingly, we stake out a middle ground. We’re going to argue that certain well-known classic strategies that have worked

Models beat experts—or, stated more cautiously, models typically beat experts. This is the rallying cry of DIY Financial Advisor: A Simple Solution to Build and Protect Your Wealth (Wiley, 2015) by Wesley R. Gray, Jack R. Vogel, and David P. Foulke, all managing members of Alpha Architect. Whether

Does the Labor Day holiday, marking the end of summer vacations, signal any unusual return effects by refocusing U.S. stock investors on managing their portfolios? By its definition, this holiday brings with it any effects from the turn of the month. To investigate the possibility of short-term

Horrific Performance An initial investment of more than $450,000 to the ProShares Ultra VIX Short-Term Futures ETN (UVXY) at the open of its October 4th, 2011 inception date (the split adjusted opening price) would be worth just $87 at today's close (this after a more than 28% gain today and

According to the Efficient Market Hypothesis, stock prices reflect all available information, and past stock price movements should have no bearing on future average returns. Yet academic research has found evidence of certain quantifiable factors that can be predictive of future returns.

We are happy to announce that our second book, DIY Financial Advisor, is finally available. For a limited time (and while supplies last) we are selling the book direct for $14.99! To get this deal you need to buy from the link below the main Amazon link. The first part of the book is dedicated to

Financial Applications Within the Monte Carlo realm a vast number of applications exist. In this final part I bring together all the previous work as well as put into practice the theory we have gathered so far. Applying the Metropolis-Hastings Algorithm From the previous section we deduced a way in

Summary In 2015, we’ve seen 40 “1%” days – days where the market was up or down at least 1% – in the S&P 500 Since 1958, the S&P 500 has experienced, on average, 54 1% days Being currently below average does not imply we should expect to see more volatility in the fall We’ve

The Ivy Portfolio spreadsheet track the 10 month moving average signals for two portfolios listed in Mebane Faber’s book The Ivy Portfolio: How to Invest Like the Top Endowments and Avoid Bear Markets. Faber discusses 5, 10, and 20 security portfolios that have trading signals based on long-term

Notable on Friday was that the 50-day moving average of the SPX closed below its 200-day moving average. This is often referred to as a “Death Cross”. (When the 50ma is above the 200ma that is a “Golden Cross”.) This is the first Death Cross since early 2012. Let’s take a brief look at

Macroeconomic forecasting is incredibly difficult. The results from this paper suggest that the brainpower of the Fed’s 100 person economics team can predict 3 to 6 months out with a reasonable degree of success, but beyond that time horizon (e.g., 1-year), basic forecasting models perform just as

Recently Big 'O' Sharpe scrubbed out my Steady Vol and Skewerage strategies. I've never been sentimental. Bullet to the head. Move on. But Wait! I forgot, that I once combined both strategies together, like so, weight.INDEX_SP500 = 1 / realisedVol - skewChange; and weighted on a

Supply and Demand of S&P 500 Put Options

What has happened in the past when the SPY opens 3.5% or more down? I ran the numbers and have some code for doing it yourself. I found that there's typically a profitable day ahead, and even if not profitable, the day tends to have enough upside (Open to High) to be of great interest. Here is

Bar some evolutionary improvements, the Lazy Backtest IDE is now about as efficient as it is possible to be. This enables me to introduce the latest feature - Big 'O' analytics. The IDE generates multiple backtesting results in the background by changing the starting dates of backtests.

The best quant mashup links for the week ending Saturday, 08/29 as voted by our readers: A New Harry Long Strategy, And Plans For Hypothesis-Driven Development [QuantStrat TradeR] Performance of Two Strategies in Momersion Regimes [Price Action Lab] Quant-Trader or Trader-Quant? [MKTSTK] Combining

Low-Beta Investment Strategies

Persistency of the Momentum Effect: The Role of Consistent Winners and Losers

Principal Component Analysis of High Frequency Data

Large-Dimensional Factor Modeling Based on High-Frequency Observations

Markov Chains, Central Limit Theorem and the Metropolis-Hastings In the previous article I gave a generic overview of Monte Carlo as well as introduced importance sampling. We now dive deeper by giving strict definitions of some of the widely used and yet misunderstood or rather commonly neglected

Last time we showed how to estimate a CCC and DCC volatility model. Here I describe an advancement labored by Engle and Kelly (2012) bearing the name: Dynamic equicorrelation. The idea is nice and the paper is well written. Departing where the previous post ended, once we have (say) the DCC

1. Motivation Evolutionarily Slow. In modern financial markets, people simultaneously trade the exact same assets on vastly different timescales. For example, a Jegadeesh and Titman (1993)-style momentum portfolio turns over half its holdings once every 6 months. By contrast, Kirilenko, Kyle,

Big 'O' Sharpe changes backtest starting dates day by day until the lowest Sharpe is found. When strategies rebalance on periodic basis it turns out that such very small changes cause very large differences in results. Big 'O' Sharpe is the pessimistic grumpy brother of the

This daily indicator is calculated as the ratio of the number of S&P500 stocks that have reached new 3-month-highs minus those that have reached new 3-month-lows, divided 500. Exiting and entering the stock market according the indicator’s signals would have avoided major drawdowns of the

How crazy is current market action? Not that crazy. …and if you lived through 2008, definitely not that crazy. Seeing a -3%+ or a +3% observation is roughly a 1/100 event, or ~ 2.5 times a year. Obviously, return events are not independent and volatility tends to cluster, but the numbers above

Yesterday I looked at stock market returns in the week and month after a large daily decline and found that it is usually a good time to buy more equities. Especially because, as long-term investors, our strongly held prior is that equity markets appreciate over time. But what about spikes? Do large

Numerous marketing pieces circulating around the web show the detriment that trying to time the market can have on a portfolio. These pieces often look similar to this chart, which shows the cumulative growth of $1 invested in the S&P 500 ETF (SPY) assuming that a given number of best days are

Thursday’s rally was accompanied by the lightest volume in 5 days. The relatively low volume could be worrisome for bulls. The importance of volume can be seen in the studies below. The first one looks at 2%+ SPX gains when volume comes in relatively high. 2015-08-28 image1 A week later ¾ of the

There's an infinite number of ways to plot financial time series, let's look at the main ones. The most basic way is just plonking returns on a plot. This has one very nice feature. The returns are comparable across time, which makes a lot of sense, right? A return at the beginning of our

I tweeted a few days ago that I had big news–huge news–gigantic news about the trading course, and I do. I have been very pleased with the reception the course has gotten, and I’ve heard from many traders that it has been a pivotal piece in their development. I decided that the time has come

The study below is one that appeared in the Quantifinder yesterday afternoon. There were a few like it. This study looks at big gaps up from 50-day lows that go unfilled and close above the open. 2015-08-27 image1 The suggestion here is that the overwhelming 1-day bullishness (big gap and move

The last week has been interesting. Not always fun but at least always interesting. Extreme moves in the market are something of a double-edged sword when it comes to learning. First, extreme moves are "special". Obviously so in terms of frequency, but also in terms of the investor

I recently rediscovered the Timely Portfolio post on R Financial Time Series Plotting. If you are not familiar with this gem, it is well-worth the time to stop and have a look at it now. Not only does it contain some useful examples of time series plots mixing different combinations of time series