40 Essential Time Series Interview Questions: Insights from the SkillPower DataFest 2017

Time series analysis is a crucial skill for data scientists, especially those working on problems in forecasting, anomaly detection, and sequence modeling. But it‘s also an area where many candidates struggle, due to the complexity of the mathematical concepts and the wide range of techniques involved.

To help data scientists assess and improve their time series skills, the SkillPower DataFest 2017 compiled a set of 40 interview questions covering everything from basic definitions to advanced modeling. In this post, we‘ll dig into the key concepts, walk through some of the trickiest problems, and highlight common pitfalls. Whether you‘re preparing for interviews or just looking to boost your time series knowledge, read on for insights that will help you level up.

Key Concepts in Time Series Analysis

Before diving into the problems, let‘s review some of the core concepts you‘ll need to master for time series interviews.

Stationarity and Differencing

A time series is said to be stationary if its statistical properties like the mean and variance are constant over time. Stationarity is a common assumption of many time series models, but real-world data often violates it. For example, a time series with an upward trend or changing variance would be non-stationary.

One way to handle non-stationary series is differencing: computing the differences between consecutive observations. First-order differencing can remove a linear trend, while second-order differencing can remove a quadratic trend. The ACF plot of a non-stationary series will decay slowly, while the ACF of a stationary series will drop to zero relatively quickly.

Seasonality and Seasonal Decomposition

Seasonality refers to patterns that repeat at fixed intervals, such as daily, weekly, or annual cycles. Identifying and modeling seasonal patterns is a key part of many time series problems. Seasonal decomposition techniques can separate a time series into trend, seasonal, and residual components.

Some common indicators of seasonality include spikes in the ACF plot at seasonal lags and a repetitive pattern in the time series plot. Seasonal differencing, which computes the difference between an observation and the previous observation from the same season, can be used to make a seasonal series stationary.

Autocorrelation and Partial Autocorrelation

Autocorrelation measures the linear relationship between lagged values of a time series. The ACF plot shows the autocorrelation at different lags. Partial autocorrelation also measures the relationship between a series and its lags, but it controls for the values at lower-order lags.

The patterns in the ACF and PACF plots can help identify suitable models for a time series. For example, an AR(p) process will have a gradually decaying ACF and a PACF that cuts off after lag p, while an MA(q) process will have an ACF that cuts off after lag q and a gradually decaying PACF.

Relation to Machine Learning and AI

Time series analysis is closely related to several areas of machine learning and AI, including:

• Sequence modeling: Many ML tasks involve predicting or generating sequences, such as language translation, speech recognition, and music generation. Techniques like recurrent neural networks (RNNs) and long short-term memory (LSTM) networks are commonly used for these problems.

• Anomaly detection: Identifying unusual patterns or outliers in time series data is important for applications like fraud detection, system monitoring, and predictive maintenance. ML algorithms like isolation forests and autoencoders can be used for time series anomaly detection.

• Reinforcement learning: In reinforcement learning, an agent learns to make a sequence of decisions based on rewards from its environment. The sequence of states, actions, and rewards can be modeled as a time series. Techniques like temporal difference learning and Q-learning are used to train RL agents.

Understanding the connections between time series analysis and these related areas can help you develop a more holistic view of the field and identify opportunities to apply techniques across domains.

SkillPower DataFest 2017: Overview and Insights

The 40 questions in the SkillPower DataFest cover a wide range of time series topics, from basic concepts to advanced modeling techniques. Here are some key themes and insights that emerged from the problem set:

• Importance of stationarity: Several questions focus on identifying non-stationary series and applying techniques like differencing and decomposition to achieve stationarity. This highlights the importance of stationarity as a fundamental assumption of many time series models.

• Role of ACF/PACF plots: Many problems require interpreting ACF and PACF plots to identify model parameters or assess stationarity. Familiarity with the characteristic patterns of different models is essential.

• Model selection: Multiple questions touch on choosing between different time series models, such as AR vs MA or seasonal vs non-seasonal ARIMA. Information criteria like AIC and BIC are commonly used for model selection.

• Forecasting and prediction intervals: Several problems deal with generating forecasts from time series models and assessing their accuracy. Understanding concepts like prediction intervals and measures like MAPE is important for forecasting applications.

Overall, the DataFest questions emphasize a blend of theoretical knowledge and practical problem-solving skills. Successful candidates need to be comfortable with both the mathematical foundations of time series analysis and the hands-on aspects of working with real data.

Deep Dive: Solving Time Series Interview Problems

Now let‘s walk through a few of the more challenging DataFest problems and break down the key insights.

Question 31

Consider the following AR(1) model with the disturbances having zero mean and unit variance:

yt = 0.4 + 0.2yt-1 + ut

The unconditional variance of y will be:

A) 1.5 B) 1.04 C) 0.5 D) 2

To solve this, we need to recall the formula for the unconditional variance of an AR(1) process:

Var(yt) = σ^2 / (1 – ϕ^2)

where σ^2 is the variance of the white noise process ut and ϕ is the autoregressive coefficient.

Here, σ^2 = 1 and ϕ = 0.2. Plugging these in gives:

Var(yt) = 1 / (1 – 0.2^2) = 1 / 0.96 ≈ 1.04

So B is the correct answer. This question tests your ability to recall and apply a specific formula. In interviews, it‘s important to memorize key formulas so you can quickly solve problems like this.

Question 36

The figure below shows the estimated autocorrelation and partial autocorrelations of a time series of n = 60 observations. Based on these plots, we should:

A) Transform the data by taking logs
B) Difference the series to obtain stationary data
C) Fit an MA(1) model to the time series

The ACF plot shows a strong autocorrelation that declines slowly, while the PACF has a large spike at lag 1 but then declines. This pattern suggests a non-stationary series, since the ACF does not quickly drop to zero.

Answer A is incorrect because taking logs is used to stabilize the variance of a series, but it does not remove a trend or make a series stationary. Answer C is wrong because an MA(1) model would have a large spike in the ACF at lag 1 but smaller spikes at other lags, which is not the pattern we see here.

Therefore, B is the correct answer. Differencing the series can help remove the trend and make the series stationary. After differencing, the ACF and PACF plots would likely show patterns more consistent with an ARMA model.

This question demonstrates the importance of being able to identify non-stationary series and understand appropriate techniques for making them stationary. It also requires recognizing the characteristic ACF/PACF patterns of different models.

Results Analysis and Benchmarking Your Skills

So how did candidates perform on the SkillPower DataFest problems? The mean score was 17.13 out of 40, with a median of 19 and a mode of 19. The top score was 38.

This distribution suggests that the test was relatively challenging, with most participants answering fewer than half of the questions correctly. However, the fact that some individuals scored highly indicates that it is possible to perform well with strong preparation.

To benchmark your own skills, try taking the full set of 40 questions yourself and comparing your score to the distribution. If you score below the mean, you may need to focus on strengthening your foundational knowledge. If you score above the median, you‘re in good shape but may still have room for improvement on advanced topics.

Remember, the goal is not just to memorize answers but to deeply understand the concepts and techniques. If you get a question wrong, take the time to review the solution and identify any gaps in your knowledge.

Tips and Resources for Mastering Time Series

If you‘re looking to improve your time series skills, here are some tips and resources to help you along the way:

1. Brush up on your statistics: Many time series concepts build on foundations in probability and statistics. Make sure you have a solid understanding of topics like distributions, hypothesis testing, and regression.

2. Practice with real data: Textbook examples are helpful for learning concepts, but there‘s no substitute for working with real-world time series data. Look for datasets on sites like Kaggle or in R packages like fpp2 and try applying different techniques.

3. Use visual aids: Plots like time series decompositions, ACF/PACF, and residual diagnostics can give you valuable insights into your data and help you select appropriate models. Don‘t just rely on quantitative measures.

4. Learn a programming language: Most real-world time series analysis is done using tools like R or Python. Familiarize yourself with packages like statsmodels and forecast in Python or the tseries and forecast packages in R.

5. Study expert examples: Reading through detailed case studies and worked examples can help you understand the thought process behind solving time series problems. The FPP2 textbook by Hyndman and Athanasopoulos is a great resource.

6. Take an online course: If you prefer more structured learning, there are many online courses in time series analysis. Coursera‘s Practical Time Series Analysis covers a range of topics in R, while DataCamp offers several courses on time series forecasting in Python.

With dedication and practice, anyone can improve their time series analysis skills. The key is to work on it consistently and not get discouraged by initial challenges.

The Future of Time Series in the Age of AI

As artificial intelligence and machine learning continue to advance, they are transforming the field of time series analysis in several ways:

• Deep learning models like LSTMs and convolutional neural networks (CNNs) are achieving state-of-the-art results on tasks like forecasting and anomaly detection. These models can capture complex nonlinear patterns that traditional methods may miss.

• Automated machine learning (AutoML) tools are making it easier for non-experts to build accurate time series models by automating tasks like data preprocessing, feature engineering, and model selection.

• Transfer learning and meta-learning techniques are enabling models to learn from multiple related time series tasks and adapt quickly to new datasets with limited data.

At the same time, classic techniques like ARIMA and exponential smoothing are still widely used and are often competitive with more complex ML models. The future of time series analysis likely lies in combining insights from traditional statistical methods with the power of modern AI and ML.

As a data scientist working in time series, it‘s important to stay up-to-date with the latest developments in AI and to be open to incorporating new techniques into your toolkit. At the same time, don‘t neglect the fundamentals – a strong understanding of traditional methods will always be valuable.

Conclusion

Time series analysis is a challenging field, but one that is essential for data scientists working in domains from finance to healthcare to engineering. The 40 interview questions from the SkillPower DataFest 2017 provide a comprehensive overview of the key concepts and techniques, from stationarity and seasonality to ARIMA models and forecasting.

Mastering these skills requires a combination of theoretical knowledge and practical problem-solving ability. By reviewing the core concepts, practicing with real data, and learning from expert examples, you can build the foundation you need to excel in time series interviews and real-world applications.

As AI and machine learning continue to reshape the field, it‘s an exciting time to be working in time series analysis. By staying curious and continuously learning, you‘ll be well-positioned to tackle new challenges and make valuable contributions.

So whether you‘re preparing for your next interview or working on a time series project, remember to approach problems with a critical eye, a solid understanding of the fundamentals, and an openness to new techniques. With the right knowledge and mindset, you can become a time series expert and drive real impact in your work.