3

enter image description here

Would it be safe to regard this time series data as a white noise?

Here's the dataset I used for computing the ACF/PACF

Date

2008-05-23 0.323555

2008-10-15 0.650817

2009-03-11 -0.193327

2009-08-03 0.804656

2009-12-23 -0.675104

2010-05-19 0.879799

2010-10-11 0.661049

2011-03-04 -0.158048

2011-07-27 -0.266153

2011-12-16 0.215956

2012-05-11 0.963171

2012-10-03 -0.242493

2013-03-01 -0.493391

2013-07-24 0.356337

2013-12-13 0.856891

2014-05-09 -0.047004

2014-10-01 0.637736

2015-02-25 0.585704

2015-07-20 0.177135

2015-12-09 -0.108261

2016-05-04 0.609034

2016-09-26 0.164869

2017-02-17 0.218298

2017-07-12 -0.318918

2017-12-01 -0.587348

In case you need the data as a list,

[0.323555, 0.650817, -0.193327, 0.804656, -0.675104, 0.879799, 0.661049, -0.158048, -0.266153, 0.215956, 0.963171, -0.242493, -0.493391, 0.356337, 0.856891, -0.047004, 0.637736, 0.585704, 0.177135, -0.108261, 0.609034, 0.164869, 0.218298, -0.318918, -0.587348]

And here's the plot of the data

enter image description here

HyeongGyu Froilan Choi
  • 85
  • 1
  • 9

1 Answers1

4

In order to correctly interpret the acf/pacf one often needs to have an observed series that

  1. has no pulses
  2. has no level/step shifts
  3. has no deterministic trends
  4. has no seasonal pulses
  5. has constant error variance over time.

Post your data and we will see what your data knows. Sample size comes into play in aiding the interpretation of the acf/pacf .

EDITED AFTER RECEIPT OF DATA:

Time series analysis requires equally spaced observations with NO missing observations .... your are not equally spaced BUT nearly so ..thus I continue .

A useful model for your 25 observations is here enter image description here (3,0,0) with 1 pulse outlier at period 25 . More statistics are here enter image description here . The one anomaly at period 25 somewhat clouded your identification scheme. AUTOBOX my tool of choice autonatically identified and adjusted the anomaly ... enter image description here an easily suggested the AR(3) model

Here are the residuals from the model enter image description here and their acf enter image description here .

The Actual/Fit and Forecast graph is here enter image description here with forecasts here for the next 12 periods enter image description here

Model identification without considering anomalies is quite limited and misleading see I have correlogram ACF and PACF below for a temperature time series. Can I say it is MA(2) from ACF? What about AR? for a discussion of this.

IrishStat
  • 27,906
  • 5
  • 29
  • 55
  • I do have a very small dataset. It has 25 lines. Do you assume this is a too small a dataset? However, I tried the acf/pacf on many samples and did have similar plots as the one above. – HyeongGyu Froilan Choi Jun 21 '18 at 10:51
  • I do not assume that this is too small . Model identification is based upon the idea of separating signal and noise ... even with "small samples" this is often possible, Post on ... – IrishStat Jun 21 '18 at 11:48
  • Okay, I've posted the dataset.. Basically, it's a correlation coefficient dataset of two assets' return, with a 100-day window, of a 100-day stride. You'll see what I mean by looking at the date index. @IrishStat – HyeongGyu Froilan Choi Jun 21 '18 at 12:56
  • Wow I definitely wasn't expecting that much analysis! Thx :) – HyeongGyu Froilan Choi Jun 21 '18 at 21:52
  • Sorry to bother you once more, but could you please briefly notify how anomaly detection is carried out in this case? Maybe a keyword to look up on Google would be more than enough :) – HyeongGyu Froilan Choi Jun 21 '18 at 23:19
  • http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html will detail how to identify an anomaly GIVEN the form of the ARIMA model. The tour de force of AUTOBOX ( which I helped to develop) is that it simultaneously identifies both the ARIMA model and the nature and form of the Intervention Series ( waiting to be discovered ). Programs like auto.arima assume no interventions are needed/present as it brute-forces arima modelidentification.Of course if there is no need for Interventions to be identified then a presumptive approach will often work just fine. – IrishStat Jun 21 '18 at 23:51
  • Cool, I'll check it out – HyeongGyu Froilan Choi Jun 22 '18 at 00:23