A re‐examination of analysts versus time‐series extrapolation of quarterly earnings: Superiority in accuracy and earning expectation proxy

• Published date: 01 October 2022
• Author: Tao Li,Ji Yu,Zenghui Liu
• Date: 01 October 2022
• DOI: http://doi.org/10.1002/jcaf.22571

Received: March  Accepted:  April 

DOI: ./jcaf.

RESEARCH ARTICLE

A re-examination of analysts versus time-series

extrapolation of quarterly earnings: Superiority

in accuracy and earning expectation proxy

Tao Li1Ji Yu1,2Zenghui Liu3

School of Business, The State University

ofNewYorkatNewPaltz,HawkDr,

New Paltz, New York, USA

School of Business, The City University

of New YorkLehman College,  Bedford

Park Blvd, WestBronx , USA

College of Business and Economics, The

Western WashingtonUniversity,

Bellingham, Washington ,USA

Correspondence

Ji Yu, State University of New Yorkat

New Paltz, The City University of New

YorkLehman Colleg e,  BedfordPark

Blvd West Bronx, NY , USA.

Email: yuj@newpaltz.edu

Abstract

We document findings that earning extrapolation based on seasonal random

trend (SRT) model is not inferior to analysts’ quarterly earnings forecasts, which

contradicts the belief that analysts are superior to time-series models. Our find-

ings suggest that while the frequency of analysts beating SRT extrapolations is

greater than %, the marginal accuracy improvement is weak. Analysts’ fore-

casts contain larger absolute forecast error and significant pessimistic bias than

SRT extrapolation. Prior studies attribute the superiority of analysts’ forecasts

in proxying for earnings expectation to its higher accuracy. Given that the SRT

extrapolations have lower average forecast error, we explore whether market

participants use them to develop earnings expectations. Our findings indicate

that the market anchors to analysts’ forecasts and treats SRT extrapolations as

supplemental.

KEYWORDS

analysts’ forecasts, earnings expectation, PEAD, seasonal random trend model

1 INTRODUCTION

Whether analysts’ forecasts are superior to time-series

forecasts and which earning prediction provides a bet-

ter proxy for earning expectation have been a popular

topic in accounting and finance literature since the s.

Currently, the well-accepted belief is that analysts gener-

ate superior forecasts to time-series models and provide

a better proxy for earnings expectations (Brown et al.,

). Several recent studies re-examined this old topic

(Ball & Ghysels, ; Bradshaw et al., ; Pagach &

Warr, ) and brought new evidence to challenge this

widely held belief about analysts’ superiority over time-

series models. Motivated by those new findings, we join

this re-examination by focusing on another time-series

earning prediction based on the seasonal random trend

(SRT) model. We compare the performance of this SRT

quarterly earning extrapolations with analysts’ consensus

quarterly earnings forecasts in terms of both superiority of

accuracy and suitability to proxy for earning expectations.

Our SRT extrapolation assumes that the expected differ-

ences of future quarterly earnings equal the most recently

observed seasonal differences and makes earning pro-

jections based on the most recent announced earnings.

The calculation of SRT only requires the most recent five

realized quarterly earnings, which is described as below:

̂

𝑄𝑡+𝑘 =𝑄

𝑡+(𝑄𝑡−4+𝑘 −𝑄

𝑡−4)()

where tindicates the current quarter, ̂

𝑄𝑡+𝑘 is the k-quarter

ahead of earnings forecasts extrapolation. 𝑄𝑡−4 to 𝑄𝑡are

the five most recent realized earnings. The SRT extrapo-

lation provides several advantages over the prevailing two

types of time-series models in the literature. One type of

J Corp Account Finance. ;:–. © Wiley Periodicals LLC. 123wileyonlinelibrary.com/journal/jcaf

124 LI  .

the common time-series model takes the complicated para-

metric form, mostly ARIMA-type models (Brown et al.,

;Foster,;Griffin,; Pagach & Warr, ), and

the other type of time-series model assumes an extremely

simple estimate without any calculation, for example,

random walk (RW)or seasonal random walk (SRW) (Brad-

shaw et al., ; Pagach & Warr, ). The ARIMA-type

models provide insights into the autocorrelation pattern;

however, they also suffer from many caveats. First, analy-

ses based on ARIMA models are subjected to survivorship

biases. To achieve a stable parameter fit, a long track of

earnings records is needed, which casts a significant loss

to the qualified stocks.In addition, satisfying the assump-

tion of stationarity in the ARIMA model can result in a

further loss of data if certain stocks do not meet the sta-

tionary assumption (Bao et al., ). Therefore, the sample

in the studies that employed ARIMA analyses is biased

toward large, mature stocks with stable earning processes.

Second, many empirical studies using ARIMA models gen-

erally adopted a unified model specification about the

order of autoregressive, differencing, and moving averages

for all firms. This unified model specification has potential

issues of model misspecification. Although, diversified,

unique processes can be generated for each firm, there is

still a risk associated with overfitting and overusing data

in doing so (Griffin, ). Due to the constraint of data

availability and restrictive statistical assumptions, earning

predictions generated from ARIMA models may be accu-

rate but lack the basis for investors to develop earnings

expectations. In contrast, RW or SRW earnings forecasts

simply take the lag- or lag- realized quarterly earnings.

This simplification relaxes the data restrictions; however,

it also brings its own caveat of being too simple to formu-

late earnings expectations. RWmakes earnings projections

based on the most recent announced earnings and ignores

the seasonality of earnings pattern. SRW uses lag- quar-

terly earnings to account for seasonality but misses the

most important information contained in the lag- quar-

terly earnings. As getting the past quarterly becomes very

easy at no cost,market participants, regardless of insti-

tutional investors or retail investors, should make use of

the readily available data to develop earnings expectations.

In this sense, we propose the SRT extrapolation measure

should be superior to both ARIMA models and RW/SRW

models, as it addresses most issues associated with

them.

Based on the quarterly earnings of US companies, we

perform empirical analyses across a -year sample period

between  and  to assess the following two research

questions: () which earning prediction is more accurate;

and () which earning prediction provides a superior proxy

for earnings expectation. To answer the first question,

we compare the accuracy of analysts’ quarterly earnings

forecasts with that of SRT extrapolations overvarious hori-

zons, ranging from  to  quarter-ahead toward the actual

earnings announcement. Weconsider analysts’ superiority

of accuracy by two measures. The first measure consid-

ers the proportion of analysts being more accurate than

the SRT extrapolation. The second measure considers the

magnitude of accuracy superiority by taking the differ-

ence of the price-scaled absolute forecast errors between

analysts and SRT extrapolations. Analysts’ forecasts have

one distinct difference from the time-series model: ana-

lysts’ forecasts are dynamic, and time-series extrapolations

are static. Analysts continuously monitor the information

about their covered stocks and provide frequent updates

on the earnings forecasts. Therefore, we assess analysts’

advantage of utilizing the new information by compar-

ing the forecasts accuracy at different time points during

the fiscal quarter. In addition to forecast accuracy, the

bias of forecast is another critical measure of the forecast

quality. Analysts’ annual earnings forecasts are gener-

ally believed to be optimistically biased (Bradshaw, ).

However, their quarterly forecasts may have a different

pattern due to analysts’ incentive of currying favor with

firm management by issuing beatable estimates (Ke &

Yu, ). Therefore, we also compare the bias pattern

between analysts and SRT extrapolations. Last, we employ

a regression analysis to examine several determinants of

analysts’ superiority of accuracy.

We document several important findings related to our

first research question. First, we find that analysts’ con-

clusion is more accurate than the time-series model is not

entirely correct. We find supporting evidence that the pro-

portion of analysts beating SRT is significantly greater than

% using our first accuracy measure. However, we also

discover that the average of absolute forecast errors of SRT

extrapolation is statistically lower than that of analysts’

forecasts. Given the two pieces of conflicting evidence, the

question about analysts’ superiority of accuracy should be

inclusive. Second, consistent with analysts having infor-

mation and timing advantage (Bradshaw et al., ), we

find that analysts keep increasing the accuracy through-

out the fiscal quarter. Right after earning announcement,

only .% of records are associated with analysts being

more accurate than SRT extrapolation; however, this pro-

portion reaches .% by the last day before the upcoming

earning announcement. Third, in terms of forecast bias,

SRT extrapolation is much superior to analysts’ consensus

forecasts. Analysts exhibit severe pessimistic bias in one-

quarter-ahead forecasts, but SRT extrapolation remains

consistently unbiased. Our complete examination of the

forecast accuracy and bias lends strong evidence to support

that SRT extrapolation is not inferior to analysts’ forecasts.