#### Degree

Doctor of Philosophy

#### Program

Statistics and Actuarial Sciences

#### Supervisor

Dr.A. Ian McLeod

#### Abstract

Environmental data is frequently left or right censored. This is due to the fact that the correct value for observed values that are below or above some threshold or detection point are inaccurate so that it is only known for sure that the true value is below or above that threshold. This is frequently important with water quality and air quality time series data. Interval censoring occurs when the correct values of the data are known only for those values falling above some lower threshold and below some upper threshold. Censoring threshold values may change over time, so multiple censor points are also important in practice. Further discussion and examples of censoring are discussed in the first chapter. A new dynamic normal probability plot for censored data is described in this chapter. For some environmental time series the effect of autocorrelation is negligible and we can treat the data or often the logged data as a random sample from a normal population. This case has been well studied for more than half a century and the work on this is briefly reviewed in the second chapter. The second chapter also contains a new derivation and a new algorithm based on the EM algorithm for obtaining the maximum likelihood estimates of the mean and variance from censored normal samples. A new derivation is also given for the observed and expected Fisher information matrix. In chapter three the case of autocorrelated time series is discussed. We show the close relationship between censoring and the missing value problem. A new quasi-EM algorithm for missing value estimation in time series is described and it efficacy demonstrated. This algorithm is extended to handle censoring in the general case of multiple censor points and interval censoring. When there is no autocorrelation, this algorithm reduces to the algorithm developed in Chapter 2. An application to water quality in the Niagara river is discussed.

#### Recommended Citation

Mohammad, Nagham Muslim, "Censored Time Series Analysis" (2014). *Electronic Thesis and Dissertation Repository*. 2489.

http://ir.lib.uwo.ca/etd/2489