Time series analysis of discourse: A case study of metaphor in psychotherapy sessions

Abstract

Time series analysis (TSA) is a technique to describe the structure and forecast values of a particular variable based on a series of sequential observations. While commonly used in finance and engineering to understand structural changes across time, its applicability to humanistic processes like discourse is less clear. This article demonstrates the feasibility and complementary use of TSA with a case study of metaphor use in psychotherapy sessions. A conceptual sketch of how TSA components (trends, seasons, cycles and irregular fluctuations) relate to discourse components is followed by a step-by-step analysis of two therapist–client dyads. Each dyad is shown to be adequately described by a different model, and the key characteristics of the models are interpreted alongside prior qualitative analysis of the dyads, shedding new light on their structural properties and attendant implications. Limitations of the present analysis and future research directions are briefly discussed.

Determination of Remaining Useful Life in Cyclic Processes

“…Using time series becomes advantageous in cases where the observed data set presents constant structural changes, i.e., when the internal components of time series have constant variability. 16,17 In general, a time series is composed of one or more terms of eq 24:…”

“…18 The seasonality component is present in the time series when it presents repetitive periodic movements, being modeled as sine waves of known period m. By autocorrelation, it is possible to know the size of period m because seasonal series present high autocorrelation in multiple lags of period m. One of the objectives of the time series analysis is to look for relevant periodicity in the data; in addition, autocorrelation and partial autocorrelation are useful for determining the order of autoregressive models. 17,19 The following are three methods for modeling the time series that consider trend and seasonality. First, the concept of stationarity will be presented, after which a simple method will be presented, which is the simple exponential smoothing, followed by the double exponential smoothing that captures the trend characteristic, and finally, the triple exponential smoothing, which encompasses both the trend of the time series and the seasonal component.…”

“…For example, the correlation in lag 3 is between time values equal to t and t + 3, removing the effects of the values in t + 1 and t + 2. 17 Another method to identify a stationary process is the augmented Dickey−Fuller test (ADF). The ADF test assumes that in the presence of autocorrelation, the first-order differentiation, x t ′, of a time series x t can be expressed as a linear regression of previous time instants and first-order differences up to a lag of k instants of time.…”

“…This methodology consists of predicting future values of a process based on past values, exploring the dependence between successive observations, autocorrelation, and partial autocorrelation, over time. Using time series becomes advantageous in cases where the observed data set presents constant structural changes, i.e., when the internal components of time series have constant variability. , …”

“…The partial autocorrelation (PACF) is similar, but removing the influence of intermediate variables. For example, the correlation in lag 3 is between time values equal to t and t + 3, removing the effects of the values in t + 1 and t + 2 …”