Category: Data Science

Mala Mahadevan covers some basics of probability:

Probability is an important statistical and mathematical concept to understand. In simple terms – probability refers to the chances of possible outcome of an event occurring within the domain of multiple outcomes. Probability is indicated by a whole number – with 0 meaning that the outcome has no chance of occurring and 1 meaning that the outcome is certain to happen. So it is mathematically represented as P(event) = (# of outcomes in event / total # of outcomes). In addition to understanding this simple thing, we will also look at a basic example of conditional probability and independent events.

It’s a good intro to a critical topic in statistics.  If I would add one thing to this, it would be to state that probability is always conditional upon something.  It’s fair to write something as P(Event) understanding that it’s a shortcut, but in reality, it’s always P(Event | Conditions), where Conditions is the set of assumptions we made in collecting this sample.

Alex Smolyanskaya explains some common errors when doing time series analysis:

Non-zero model error indicates that our model is missing explanatory features. In practice, we don’t expect to get rid of all model error—there will be some error in the forecast from unavoidable natural variation. Natural variation should reflect all the stuff we will probably never capture with our model, like measurement error, unpredictable external market forces, and so on. The distribution of error should be close to normal and, ideally, have a small mean. We get evidence that an important explanatory variable is missing from the model when we find that the model error doesn’t look like simple natural variation—if the distribution of errors skews one way or another, there are more outliers than expected, or if the mean is unpleasantly large. When this happens we should try to identify and correct any missing or incorrect model features.

It’s an interesting article, especially the bit about cross-validation, which is a perfectly acceptable technique in non-time series models.

Vincent Granville shows a simple technique for removing auto-correlation from time series data:

A deeper investigation consists in isolating the auto-correlations to see whether the remaining values, once decorrelated, behave like white noise, or not. If departure from white noise is found, then it means that the time series in question exhibits unusual patterns not explained by trends, seasonality or auto correlations. This can be useful knowledge in some contexts  such as high frequency trading, random number generation, cryptography or cyber-security. The analysis of decorrelated residuals can also help identify change points and instances of slope changes in time series.

Dealing with serial correlation is a big issue in econometrics; if you don’t deal with it in an Ordinary Least Squares regression, your regression will appear to have more explanatory power than it really does.

Steph Locke answers an important question related to time series:

Additive or multiplicative?

It’s important to understand what the difference between a multiplicative time series and an additive one before we go any further.

There are three components to a time series:
– trend how things are overall changing
– seasonality how things change within a given period e.g. a year, month, week, day
– error/residual/irregular activity not explained by the trend or the seasonal value

How these three components interact determines the difference between a multiplicative and an additive time series.

Click through to learn how to spot an additive time series versus a multiplicative.  There is a good bit of very important detail here.