{
  "source_file": "0930",
  "source_platform": "Medium",
  "author": "Ransaka Ravihara",
  "title_listed": "Introduction to time series data",
  "keywords": "时间序列,预测",
  "domain": "数据处理",
  "content_type": "深度技术解析",
  "is_paid_flag": "部分免费/会员墙",
  "url": "https://towardsdatascience.com/understand-the-time-series-data-cd9746d3df62/",
  "publish_date": "2022-04",
  "corpus_stage": "预训练/SFT",
  "notes": "",
  "id": "585d31a92732",
  "collected_at": "2026-10-01T23:42:44",
  "title": "Introduction to time series data | Towards Data Science",
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It also helps in adverstising on the website.\n\n\n  * Cookie\nedgebucket\n  * Duration\nsession\n  * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n  * Cookie\ndid\n  * Duration\n1 year\n  * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Data Science](https://towardsdatascience.com/category/data-science/)\n# Introduction to time series data\nAn introduction to using time series data for forecasting problems\n[Ransaka Ravihara](https://towardsdatascience.com/author/ransakaravihara/)\nApril 13, 20225 min read\n![Photo by Icons8 Team on Unsplash](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/0ad_PdLl709B3asK3-scaled.jpg)\nPhoto by [Icons8 Team](https://unsplash.com/@icons8?utm_source=medium&utm_medium=referral) on [Unsplash](https://unsplash.com?utm_source=medium&utm_medium=referral)\nIn simple words, time series is a sequence of data points that are ordered according to timestamp. Hence, time series modeling required a special method compared to traditional machine learning approaches. Because, in time series modeling, we can't just neglect the order of the data points.\n* * *\n**Introduction**\nAs always, it's important to have an understanding about what is the underlying pattern of our dataset. Let's begin with a simple time series.\nLearn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) roadmap.\n![Wikipedia daily visitors - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1b_Oi36fHc5JBxvHaqo9ISg.png)\nWikipedia daily visitors - Image by Author\nWithout considering any standard time series concepts, let's find out what we can see in the above plot.\n  * There is a negative slope from 2018-Jan to 2018-Aug and then, a positive slope from 2018-Aug to 2019-Jan\n  * If we concentrate on only one month (or a few months), we can see there is a constant pattern in the dataset throughout the entire time period. That is, there are 2 or 3 valleys and peaks that have been recorded for each month.\n\n\nThe above conclusions depend on the way we look at the above plot. For someone who has a different viewpoint than me, definitely would see some useful information by looking at the above plot. Hence, it's important to derive information in some standard way. One of the best ways to do so is to plot the dataset.\nIn R, there are plenty of time series visualization methods available to use. But in Python, sometimes we need additional work to do.\nLet's zoom into 2 months' data.\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1ASlrbGKL8VwjLFM6ECTySg.png)\nImage by Author\nWell, for clear understanding let's indicate weekends.\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1QssguqSP5cyhdkW1vKAmkQ.png)\nImage by Author\nThere is a clear pattern in the dataset. That is,\n  * The highest page view count always (at least in used time period) was recorded on Monday.\n  * Lowest pageview count is always recorded on Saturday.\n  * In most weeks, there is a spark in the middle of the week.\n\n\nSo far, we have seen the properties of the dataset. Now it's time to move to real-time series concepts.\n* * *\nIn the previous section, we identified that there are slope and repeating patterns in the dataset. This means, our time series can be split into several components or we can \"**Decompose** \" the time series. Let's dive into methods that we can use to decompose the time series.\n**Time series decomposition**\nUnlike other data, time series data can be really confusing. As an example, here is the Sri Lankan president's Wikipedia profile view after he was elected as president.\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1KMt5YWjyIDUPGHqCFxcyjQ.png)\nImage by Author\nAs you can see here, time series data can be influenced by various factors. That's why we need to decompose it and understand it well. It also helps to increase the accuracy of the predictions.\nMost time series consist of **Seasonal Component** ( In the previous section, we identified this as valley and peaks), **Trend Component** (Previously we identified this as slope). When these two components are removed from the original data, we have an **Error Component**. But the problem is, how do we split these components without knowing how these components are formed? Before answering this question, it's important to know possible decomposition methods available.\n  1. Moving Average based decomposition\n  2. Classical decomposition\n  3. X11 decomposition (Enhanced method of classical decomposition)\n  4. SEATS decomposition (**S** easonal **E** xtraction in **A** RIMA **T** ime **S** eries)\n\n\nFor simplicity, let's continue with the classical decomposition method. In classical decomposition, there are two types of methods.\n### 1. Additive decomposition\nIn additive decomposition, we assume **original series(y)** can be constructed using adding S**easonal Component(S)** , **Trend Component(T)** & **Error Component(R)** together.\n![Additive decomposition formula - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1MkJLWJoQ3WDduEnTYuR5ew.png)\nAdditive decomposition formula - Image by Author\n**Steps :**\n  1. Estimating the trend by applying a convolution filter to the data, **Tₜ**\n  2. Calculate the detrended series. (**yₜ-Tₜ**).\n  3. Detrended series removed from original series and then calculate the average of this de-trended series for each period. This gives a Seasonal Component(**Sₜ)**\n  4. Substract **Sₜ** ,**Tₜ** from **yₜ**. This gives **Rₜ; Rₜ** = **yₜ** -(**Tₜ** +**Sₜ**)\n\n\n### 2. Multiplicative decomposition\nAs the name suggests, here we assume the original series can be constructed using multiplying **Seasonal Component** , **Trend Component** & **Error Component** together.\n![Multiplicative decomposition formula - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1GhTDIFPOB3k5TIvQRVpkAg.png)\nMultiplicative decomposition formula - Image by Author\nNow we have two possible answers to the previous question, either Multiplicative or Additive. We can use the below method to choose one method over another.\nIf the magnitude of the seasonal component increases, the time series is multiplicative. If the magnitude of the seasonal component is roughly the same, it's more likely to be an additive time series\nHere is the definition of key terms we discussed so far.\n  * **Seasonal** - Repeating patterns associated with some aspect of the calendar.\n  * **Trend** - Increasing or decreasing value in the series(Slope).\n  * **Cycle** - This term often confusing with Seasonal component. The major difference is there is no fixed period.\n\n\nNow we know the basic theories. It's time to do some coding and plotting.\n* * *\nFor that, we will be using a popular Python library called[ statsmodels](https://www.statsmodels.org/dev/index.html). Moving to the previously used Wikipedia dataset.\nWe can perform classical decomposition using, statsmodels `seasonal_decompose()` function. If you clearly see above time series, it's more similar to the additive series we discussed above. You can set model type in `seasonal_decompose()` function using `model` parameter.\ntext\n\n```\nfrom statsmodels.api.tsa import seasonal_decompose\n```\n\ntext\n\n```\ndecompose = seasonal_decompose(data,model='additive')\n```\n\nLet's plot results.\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1CTELmZ_A79rgxdBCCK4rmQ.png)\nImage by Author\nLet's do some experiments with results.\n  1. Plot denoised series.\n  2. Plot **seasonally adjusted** data - When Seasonal Component is removed from the original data, the rest becomes **seasonally adjusted** data. If our analysis needs to ignore seasonal influence, this approach could be more helpful. However, It strictly depends on the problem we're working on.\n  3. Residual distribution - Often helps to identify biases of the decomposition. In the above residual plot, there are low noises from 2018-Aug to 2018-Oct. Analyzing residuals is useful to know how well our decomposition method is capable to split data into **Seasonal, Residual, and Trend** components. If residuals are more likely to [white noises](https://machinelearningmastery.com/white-noise-time-series-python/#:~:text=A%20time%20series%20is%20white%20noise%20if%20the%20variables%20are,other%20values%20in%20the%20series.), then it's the evidence that decomposition method has distinguished the components successfully.\n\n\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1YuAUGNIZYVEkg8tPcWnH7w.png)\nImage by Author\nJust for experiment purposes let's run exact same experiments with `model='multiplicative'`\ntext\n\n```\ndecompose_multi = seasonal_decompose(data,model='multiplicative')\n```\n\nDecompose results.\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1yjg-95PZkFuQIhalYm1qlQ.png)\nImage by Author\nExperiment results.\n![Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/04/1Gw62GdQhLnDB2JJvSO9zDg.png)\nImage by Author\nAs a summary of the above experiments, we can say additive decomposition is the best fit for this dataset. We can identify this by only looking at residual plots also. In additive approach, error is roughly normally distributed. This implies that our assumption is correct in this dataset.\n## Conclusion\nThe decomposition used here is classical decomposition (naïve decomposition) and it's not recommended for more sophisticated datasets.\nThanks for reading!!\n### References\n  * [Forecasting: Principles and Practice](https://otexts.com/fpp2/).\n  * [Is my time series additive or multiplicative?](https://www.r-bloggers.com/2017/02/is-my-time-series-additive-or-multiplicative/)\n\n\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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