This afternoon I had a chance to access a dataset curated from Zillow data from which it was possible to compute average home prices for several regions in the Greater Pittsburgh Area. Given that this data was available from 1996 onward to 2017, naturally I was curious to see whether the average home prices have in-fact increased across all regions in the area, considering years leading up to the real-estate crash of 2008. To remind those unfamiliar with this event, on December 30, 2008, the Case-Shiller home price index reported its largest price drop in its history. The unique dataset at my disposal this afternoon formed the ideal platform to truly examine the effects of the crash on Pittsburgh, PA.  The plot on the Left compares the year-on-year rate of change of average home price (i.e. the "Slope" of average home price, measured in "$ per year" - a term we will use throughout the remainder of this blog post) in all regions put together, leading up to Dec 30, 2008 and after the crash (i.e. considering trends from 2009 to 2017).I'll have to say I was a little disappointed to see such a marginal increase in the Slope of year-on-year average home value - while there was an improvement, it was hardly statistically significant when the entire cohort is considered.

But this can't be right, per common knowledge, can it?  I thought the market was doing better of-late, given the skyrocketing home prices these days. A colleague and mentor of mine once told me that a limited dataset will confess to anything if interrogated sufficiently.  So, I decided to tear the data apart a little bit more to make it confess to what I wanted it to tell me.  Onward to Exhibit #2 (see below; click to zoom in):

From the plot above, which describes the change in Slope of average home value by region from before Dec 30, 2008 to after this point in time (viz. the X-axis), it seems quite clear that there were several regions in the Greater Pittsburgh Area which did in-fact start improving in region-average home price after the crash of 2008 - but some better than others. Contrary to common thought, there were a host of regions which actually started doing "worse" after 2009 than they were doing before the crash.  What in the world did these regions have to do in order to accomplish this?  Lets find out! In the plot below, I examine how the year-on-year rate of change in home value (i.e. the Slope) after the crash relates to the change in Slope from before the crash to after the crash, such that each circle in the plot below represents a region, the size of which is equivalent to the relative average home value in that region.  Further, to add information to this plot, the plotted circles are heat-mapped from light-blue to black in increasing order of Slope of year-on-year home value "before" the crash.  So, what does this tell us?

Well, it appears as though the regions which were actually doing well up until the crash of 2008 started doing really poorly with a year-on-year decrease in average home value after the crash!  Au contraire, not all the regions which were doing badly before the crash started doing particularly well (in terms of slope i.e. year-on-year increase in average home price) after 2009. What is clear however is that the largest circles in the plot i.e. the regions which have the highest region-average home value today also correspond with those regions which were mid-range in terms of Slope of home value over time before the crash (i.e. light blue) but also experienced the largest change in Slope from before to after the crash of 2008 (i.e. they're on the far right of the plot above - including, Peters Township and Upper St Clair in the South of Pittsburgh, and Franklin Park and Wexford in the North)!  Oh, how the times change!

In summary, it appears that the regions which did poorly (i.e. either getting lower in value from year-to-year or pretty much changing by very small dollar amounts per year, before the Crash) began doing a whole lot better after 2009, with significantly increasing home values every year (see summary plot below), whereas all the so-called "Healthy" areas before the crash began losing in value every year (i.e. negative Slopes!) after 2009 - mind boggling, right?  Ah, but one group of elite regions before the crash did hold its own and surpassed other regions in terms of growth in value after 2009 - which one was this? Alas, the rich tend to always grow richer and the best performers since 2009 were also the best performers in terms of year-on-year home value before Dec 30, 2008.  So, it pays to go big when you're buying your "forever home"!
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As a prospective home-buyer targeting a strong school district, I look for schools a favorable student teacher ratio (<= 20:1) but also bang for my buck in terms of getting as much house per dollar, as possible!  However, the latter isn't a trivial landscape to assess as more often than not the affordability of a home is hinged on a reasonable home value for the purpose of tax assessment in addition to the alluring bells and whistles that set apart one similarly priced home in an optimal school district, from another. In this post, I analyze list price, tax assessed value and home quality in terms of interior components, as a function of school district.  

My focus in this study is homes of value between $250k and $350k, in the Riverview School District (Oakmont, PA) and the West Jeffrson Hills School District (Jefferson Hills, PA & Pleasant Hills, PA), while focusing on statistical evidence of paying optimal value per square foot of home, without compromising on schooling quality accessible in the region.  In order to do this, I wrote a PHP-based web-scraper hosted in a local WAMP environment to extricate data from the West Penn MultiList, including school-district and several fields which aren't typically accessible via any publicly available API - including the Zillow API!  For those reading this article whom are interested in my code for this, please write to me in the comments, below :)
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First, how does list price compare with tax assessed value in Oakmont as opposed to Jeffrson Hills?  Well, the plot below is clear in terms of the fact that homes in Jeffrson Hills are tax assessed in terms of a value very close to the list price of the home, whereas in Oakmont the trend indicates a substantially lower home value assessment for tax purposes in comparison to list prices.  Does this mean Oakmont homes are overpriced?  
​Maybe Oakmont homes are overpriced - but relative to what?  To truly know this answer, we need to learn more about what square footage we get for the same dollars in the two regions!
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But first, lets think about what we're paying for based on a list price...Lets remind ourselves that we're talking about a limited cohort of homes (all active listings in the two school districts in the price range of $250k to $350k, as of the first week of Sept 2017) but the data is interesting, nonetheless. When we walk into a home as a prospective home-buyer, naive to potential skeletons revealed by a thorough home inspection report, we look for granite counter tops and hardwood flooring - bells and whistles which are quite orthogonal to the primary purpose of a place of shelter (e.g.: the roof or the likelihood of the place being in a flood zone!).  Nevertheless, lets take flooring, for instance - does quality flooring increase the list price of a home?  

Moving on to square footage!  While the assessed home values are higher in Jefferson Hills and Pleasant Hills (both in the West Jeffrson School District), Jefferson Hills offers the greatest home square-footage per dollar of tax owed, by far, relative to the overpriced and relatively smaller homes in Oakmont. What Oakmont's got going for it though is that you'll probably end up paying a bit lower of a mortgage payment in Easy Allegheny owing to the lower tax assessments of its homes, relative to Jeffrson hills (South Allegheny).
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And don't forget those tiny yards in Oakmont relative to the abundance of yard space seen in homes in Jeffrson Hills!  So, in conclusion, I'd say that Jeffrson Hills would be the place to get the most bang for your buck, comparing with Oakmont's Riverview School District at least.  This does seem congruent with common knowledge though - after all, lets remind ourselves that Jeffrson Hills was rated the top place to raise a family in the Commonwealth of Pennsylvania, at one point!

This morning I had a chance to look into a dataset of 7,584 homes sold between Aug 2016 and Aug 2017, in the Greater Pittsburgh Area, from the West Penn Multi-List.  This dataset included 9 of the most desirable counties in the area and encompassed 76 unique areas (each corresponding to at least one unique school district).  The range of prices of sold homes in the area had a mean of $249,204.73 +/- 2127.51 (std dev: $185,276) with sold prices going all the way up to $2,165,000.00!  

Contrary to common belief I found that while Sold Price was a function of List Price (see Figure below) with a 70% predictive strength, the number of Full Baths were a better descriptor of the variability in Sold Price than number of Bedrooms and County put together!  
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So, how does List Price compare with Sold Price, for homes with an increasing number of bedrooms?  Clearly more expensive homes have a greater likelihood of having more bedrooms, but a really pricey home may still not be the mansion you would expect it to be, while even less expensive homes can have up to 7 bedrooms!

Typically algorithmic traders attempt to leverage historical stock prices, price movements and functions of price or volume of trades, including Twitter or Stocktwits based sentiment to predict the direction of future stock prices. Such models are often supplemented by a money management strategy which is implemented in the form of a trade execution engine that uses the historical success of predictions made by a trained model or identified pattern to determine the amount of capital to invest (i.e. in the long or short direction) on future predictions. However, all inputs to an algorithmic trading model - machine learning based or simple pattern recognition - are not made equal.  In this blog post, I example the forecast-ability of intraday and end-of-day candlesticks by examining open, high, low, close and volume data, independently as well as in combination.

The approach for this analysis was inspired by Goerg 2012 [1] which presents an adaptation of principal component analysis i.e. a novel dimension reduction technique for temporally dependent signals, utilizing a new forecastability measure, Omega. Omega is an uncertainty metric defined based on the Shannon entropy [2] of the Fourier transform of the autocovariance function of a given univariate time series (i.e. open, high, low, close or volume, in this study). In this manner, Omega therefore forms a quantitative means to separate a multivariate time series into a forecastable (Omega >> 0) and an orthogonal white noise space (i.e. Omega ~ 0).  My analysis of SPY (S&P500 ETF) are presented below.

A look into 5, 10 and 60 minute intraday candlesticks of SPY between 1 Jan 2016 and 5 Feb 2016 led to a rather surprising revelation that intraday "volumes" are a better predictor of its future value than any of the other tested univariate time series' viz. open, high, low and close series'. Surprisingly, close prices - the often recommended gold-standard price that is supposedly least affected by end-effects, instabilities and such was found to be the "least" predictable series!

Predictive maintenance - a burgeoning science - is the art of machine learning to help determine the condition of in-service equipment, usually in real-time, and therefore predict when maintenance should be performed. This approach promises cost savings over routine or time-based preventive maintenance and additionally offers the flexibility to algorithmically generate alerts which may avert catastrophic events.  

I have been involved with implementing some predictive maintenance and condition based monitoring algorithms recently, primarily with application to the transportation industry, and decided to do a little literature search on the subject: 




A above figures provide a summary of the literature in predictive maintenance space (generated based on Web Of Science search results ). The science of predictive maintenance has grown (in terms of cited and new literature) exponentially since 2014, with a remarkable performance from the transportation sector. The power of data has truly spread the wings of the transportation sector - planes, trains and automobiles - thanks to the ubiquitousness of machine learning, the virtually limitless extents of cloud storage and of course elastic cloud computing!
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It is uncanny when one finds interesting iPhone Notes from years ago. This morning I was on a random walk back through time when I stumbled into a little poem that I recall writing one morning during a visit to a Rainforest, in Puerto Rico, when there was no rain. Childish but interesting...

Rainforest , O' Rainforest
It is dry and cold outside
So, relent and harbor your time 
With the winds of tranquility ...

Reminisce the days 
Your trees danced in the rain
And raindrops broke their fall 
From stormy skies

On to your leaves,
In a million little bits
They splashed to the ground 
Nourishing flowing brooks

But it is dry and cold outside
So, relent and harbor your time 
With the winds of tranquility 
Rainforest , O' Rainforest !