# How to show trend in a Time series data set

I have 16 NDVI values for 16 years. I want to use this time series data set to investigate a trend in the dataset to distinguish between noise, randomness and actual trends.

Can I use R to do this? Or is there any other trend software for this? I just want a method that is a bit simple to understand and run as a beginner.

• There are multiple techniques, but if you just want to get your hands dirty try running an AR(1) or MA(1) process. There are a bunch of concepts like stationarity and ergodicity and order p,q but if you just want to do something simple run those – user2879934 May 1 '17 at 17:35

In order to distinguish between between random noise and actual trends it is necessary to have a model for the noise itself. For example, if the noise is Poisson type, which occurs in various counting situations like radioactive decay counting, then for $n$ counts, one expects $\sqrt{n}$ as a single standard deviation of counting error. If one expects Gaussian noise, one must have a numerical expectation of what that noise is. Subsequently, one can calculate what the fit error from the model alone is. Here is an example from EJNMMI-physics:
"Assuming counting error of a Poisson noise type, misregistration, an imaging term is defined graphically as the standard deviation vertical misalignment on a square root of count rate TAC plot, which latter is, indeed, an image. Misregistration standard deviation, $σ_M = 0.79943\%$, was calculated from the well-known equation for correlated variances $$σ_M^2=σ_{F,N}^2=σ_F^2−σ_N^2−2ρ_{F,N}σ_Fσ_N,\text{ }\text{ }\text{ }\text{ }\text{ } (11)$$ where the variance of misregistration, $σ_M^2$, is $σ_{F,N}^2$, the variance of the difference between fit error, $σ_F = 1.44164\%$ [from the standard deviation from Table 1 of Eq. (10)], and noise error, $σ_N = 1.02864\%$ [Eq. (8)], where $ρ_{F,N} = 0.76531$ is the correlation coefficient of $F$ and $N$."