noisy” data over time. A “trend” is an upwards or downwards shift in a data set over time.
In economics, “trend analysis” usually refers to analysis on past trends in market trading; it allows you to predict what might happen to the market in the future. It might, for instance, be used to predict a trend such as a bull market run.
Various tools exist to analyze trends in data. They range from the relatively simple (like linear regression) to more complex tools like the Mann-Kendall test, which may be used to search for non linear trends. Some other popular tools include:
- Autocorrelation analysis: Autocorrelation is where error terms in a time series transfer from one period to another.
- Curve-fitting: Useful for modeling specific trends. For example, you could try fitting a growth curve like a Gompertz distribution to your data.
- Filtering or Smoothing: Filtering extracts a trend from a noisy data set, while smoothing attaches “weight” (i.e. higher priority) to newer data.
- The Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test figures out if a time series is stationary around a mean or linear trend, or is non-stationary due to a unit root.
- MANCOVA (Multivariate Analysis of Covariance) is the multivariate counterpart of ANCOVA. It tells you if group differences probably happened by random chance, or if there is a repeatable trend.
- The Seasonal Kendall test (SK test) analyzes data for monotonic trends in seasonal data.
- Transformations: producing a new time series from an existing one. Useful for, say, removing a linear trend.
Most tools to model trends are one form of regression or another (Chandler & Scott, 2011). You can find dozens more trend analysis tools on the main Regression Analysis page.
Potential Weak Points in Trend Analysis
Although trend analysis can be extremely helpful in many applications—from climate change to sociological analysis—it’s important to keep in mind that it is not foolproof. In particular:
- All data (unless gathered through a population census) is liable to sampling error. The extent of this problem will increase when coarse sampling methods (e.g. convenience sampling) are used.
- Data is likely subject to measurement error; random, systematic, or external; trends in this error may be mistaken as trends in the actual data.
- “Phantom”, short term trends exist even in the most random of number sequences, so trends should be followed out as long as possible.
Also, finding no trend may mean there is no trend, but it may just as likely mean that your data is insufficient to illuminate a trend which does in fact exist.
Chandler, R. & Scott, M. (2011). Statistical Methods for Trend Detection and Analysis in the Environmental Sciences. John Wiley & Sons.
Shea, Dennis, & National Center for Atmospheric Research Staff (Eds). Last modified 05 Sep 2014. “The Climate Data Guide: Trend Analysis.” Retrieved from https://tinyurl.com/y3vfje9a on May 20, 2018.
Stephanie Glen. "Trend Analysis: Simple Definition, Examples" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/trend-analysis/
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