# Estimating the trend over time

I have series of data which is quarterly. I want to analyze is there any significance increase over time. With my little knowledge about ARIMA and time series I used auto.arima function

> auto.arima(mdr)
Series: mdr
ARIMA(0,1,1)

Coefficients:
ma1
-0.3369
s.e.   0.1329

sigma^2 estimated as 16.59:  log likelihood=-109.66
AIC=223.33   AICc=223.66   BIC=226.65


"A fitting procedure known as generalised least squares (GLS) can be used to provide better estimates of the standard errors of the regression parameters to account for the autocorrelation in the residual series." from "Paul S.P. Cowpertwait · Andrew V. MetcalfeIntroductory Time Series with R" after a search I come with to use GLS function but I couldn't understand it and how to run analysis, and whether I can use GLS function with or without differencing.

I decided to use that analysis which is in answer of Rob Hyndman to a similar question I've run auto.arima procedure which yielded with

   > auto.arima(mdr)
Series: mdr
ARIMA(0,1,1)

Coefficients:
ma1
-0.3369
s.e.   0.1329

sigma^2 estimated as 16.59:  log likelihood=-109.66
AIC=223.33   AICc=223.66   BIC=226.65

then I want to estimate the trend with x=reg function

> auto.arima(y=mdr,xreg = 1:length(mdr))
Series: mdr
Regression with ARIMA(1,0,0) errors

Coefficients:
ar1    xreg
0.7723  0.3979
s.e.  0.0988  0.1079


sigma^2 estimated as 17.11: log likelihood=-112.98 AIC=231.97 AICc=232.63 BIC=237.03

in auto.arima function data needs differencing but auto.arima function with regressors yields with different ressults

> Box.test(mdr)

Box-Pierce test

data:  mdr
X-squared = 23.967, df = 1, p-value = 9.799e-07


I am stuck in here I don't know which model to choose and how to analyze a trend of a series of a data