Lately, there has been a lot of talks whether Bitcoin is a bubble (about to burst) or not. The discussion is quite interesting, not only because there is potentially a lot of money involved, but also because it shows how our economic theories are primarily unclear and secondarily incomplete on concepts such as bubbles and… Read More »
The effects of temporal aggregation In this post I will demonstrate the effects of temporal aggregation and motivate the use of multiple temporal aggregation (MTA). I will not delve into the econometric aspects of the discussion, but it is worthwhile to summarise key findings from the literature. A concise forecasting related summary is available in… Read More »
Past experiments have demonstrated that humans (with or without formal training) are quite good at visually identifying the structure of time series. Trend is a key component, and arguably the most relevant to practice, as many of the forecasts that affect our lives have to do with potential increases or decreases of economic variables. Forecasters… Read More »
Yes and… no! First, I should say that I am thinking of the common types of neural networks that are comprised by neurons that use some type of sigmoid transfer function, although the arguments discussed here are applicable to other types of neural networks. Before answering the question, let us first quickly summarise how typical… Read More »
I was looking for an intuitive way to demonstrate to my students the need for parsimony in model building, as well as the problem of overfitting and I remembered the humorous paper by James Wel: showing that elephants are obviously created by Fourier sine series! I went a step further and implemented some popular selection… Read More »
Another interactive demo I created for the courses I teach. This one is about simple exponential smoothing and the main objective is to show the interaction between smoothing parameter and initial level in the fitting and holdout samples. A different interactive demo about exponential smoothing can be found here. A couple of points that may… Read More »
I made this little interactive demo for basic time series exploration and decomposition for my students. I uploaded it here in case someone else finds it useful. Some things to try: How does the seasonal plot looks like for seasonal and non-seasonal time series? How does the seasonal plot looks when the trend is not… Read More »
Seasonality is a common characteristic of time series. It can appear in two forms: additive and multiplicative. In the former case the amplitude of the seasonal variation is independent of the level, whereas in the latter it is connected. The following figure highlights this: Note that in the example of multiplicative seasonality the season is… Read More »
In my experience users of exponential smoothing have often limited transparency in how the various smoothing parameters interact. I built this small demo to illustrate how the different smoothing parameters and exponential smoothing components interact. You can choose between some simulated and some real time series, as well as the option to add outliers or… Read More »
Combining forecasts has been shown in many cases to lead to improvements in forecasting performance, in terms of accuracy and bias. This is also common in forecasting with neural networks or other computationally intensive methods, where ensemble forecasts are considered more accurate than individual model forecasts. A useful feature of forecast combination is that it… Read More »