What is a Time Series?

Multiple Time Series

You might need to analyze multiple time series simultaneously, e.g., sales of your brands and key competitors. Figure 2 below is an example and shows weekly sales data for three brands over a one-year period. Since sales movements of brands competing with each other will typically be correlated over time, it often will make sense, and be more statistically rigorous, to include data for all key brands in one model instead of running separate models for each brand.

Vector Autoregression (VAR), the Vector Error Correction Model (VECM) and the more general State Space framework are three frequently-used approaches to multiple time series analysis. Causal data can be included and Market Response/Marketing Mix modeling conducted.

Other Methods

There are several additional methods relevant to marketing research and data science I'll now briefly describe.

Panel Models include cross sections in a time series analysis. Sales and marketing data for several brands, for instance, can be stacked on top of one another and analyzed simultaneously. Panel modeling permits category-level analysis and also comes in handy when data are infrequent (e.g., monthly or quarterly).

Longitudinal Analysis is a generic and sometimes confusingly-used term that can refer to Panel modeling with a small number of periods ("short panels"), as well as to Repeated Measures, Growth Curve Analysis or Multilevel Analysis. In a literal sense it subsumes time series analysis but many authorities reserve that term for analysis of data with many time periods (e.g., >25). Structural Equation Modeling (SEM) is one method widely-used in Growth Curve modeling and other longitudinal analyses.

Survival Analysis is a branch of #statistics for analyzing the expected length of time until one or more events happen, such as death in biological organisms and failure in mechanical systems. It's also called Duration Analysis in Economics and Event History Analysis in Sociology. It is often used in customer churn analysis.
In some instances one model will not fit an entire series well because of structural changes within the series, and model parameters will vary across time. There are numerous breakpoint tests and models (e.g., State Space, Switching Regression) available for these circumstances.

You may also notice that sales, call center activity or other data series you are tracking exhibit clusters of volatility. That is, there may be periods in which the figures move up and down in much more extreme fashion than other periods.

In these cases, you should consider a class of models with the forbidding name of GARCH (Generalized Autoregressive Conditional Heteroskedasticity). ARCH and GARCH models were originally developed for financial markets but can used for other kinds of time series data when volatility is of interest. Volatility can fall into many patterns and, accordingly, there are many flavors of GARCH models. Causal variables can be included. There are also multivariate extensions (MGARCH) if you have two or more series you wish to analyze jointly.

Non-Parametric Econometrics is a very different approach to studying time series and longitudinal data that is now receiving a lot of attention because of #bigdata and the greater computing power we now enjoy. These methods are increasingly feasible and useful as alternatives to the more familiar methods such as those described in this article.

#MachineLearning (e.g., #ArtificialNeuralNetwork s) is also useful in some circumstances but the results can be hard to interpret - they predict well but may not help us understand the mechanism that generated to data (the Why). To some extent, this drawback also applies to non-parametric techniques.

Most of the methods I've mentioned are Time Domain techniques. Another group of methods known as Frequency Domain, plays a more limited role in Marketing Research.

❇️ @AI_Python_EN

Data science is not #MachineLearning .
Data science is not #statistics.
Data science is not analytics.
Data science is not #AI.

#DataScience is a process of:
Obtaining your data
Scrubbing / Cleaning your data
Exploring your data
Modeling your data
iNterpreting your data

Data Science is the science of extracting useful information from data using statistics, skills, experience and domain knowledge.

If you love data, you will like this role....

solving business problems using data is data science. Machine learning/statistics /analytics may come as a way of the solution of a particular business problem. Sometimes we may need all to solve a problem and sometimes even a crosstabs may be handy.

➡️ Get free resources at his site:
www.claoudml.com

❇️ @AI_Python_EN

What Are "Panel Models?"​ Part 1

In #statistics, the English is sometimes as hard as the math. Vocabulary is frequently used in confusing ways and often differs by discipline. "Panel" and "longitudinal" are two examples - economists tend to favor the first term, while researchers in most other fields use the second to mean essentially the same thing.

But to what "thing" do they refer? Say, for example, households, individual household members, companies or brands are selected and followed over time. Statisticians working in many fields, such as economics and psychology, have developed numerous techniques which allow us to study how these households, household members, companies or brands change over time, and investigate what might have caused these changes.

Marketing mix modeling conducted at the category level is one example that will be close to home for many marketing researchers. In a typical case, we might have four years of weekly sales and marketing data for 6-8 brands in a product or service category. These brands would comprise the panel. This type of modeling is also known as cross-sectional time-series analysis because there is an explicit time component in the modeling. It is just one kind of panel/longitudinal analysis.

Marketing researchers make extensive use of online panels for consumer surveys. Panelists are usually not surveyed on the same topic on different occasions though they can be, in which case we would have a panel selected from an online panel. Some MROCs (aka insights communities) also are large and can be analyzed with these methods.

The reference manual for the Stata statistical software provides an in-depth look at many of these methods, particularly those widely-used in econometrics. I should note that there is a methodological connection with mixed-effects models, which I have briefly summarized here. Mplus is another statistical package which is popular among researchers in psychology, education and healthcare, and its website is another good resource.
Longitudinal/panel modeling has featured in countless papers and conference presentations over the years and is also the subject of many books. Here are some books I have found helpful:

Analysis of Longitudinal Data (Diggle et al.)
Analysis of Panel Data (Hsiao)
Econometric Analysis of Panel Data (Baltagi)
Longitudinal Structural Equation Modeling (Newsom)
Growth Modeling (Grimm et al.)
Longitudinal Analysis (Hoffman)
**Applied Longitudinal Data Analysis for Epidemiology (Twisk)**

Many of these methods can also be performed within a Bayesian statistical framework.

❇️ @AI_Python_EN