Cultural Differences in the Estimation of Judgmental Prediction Intervals for Time Series

Cultural Differences in the Estimation of Judgmental Prediction Intervals for Time Series

Summer Xia Meng Prof. Paul Goodwin Dr. Sheik Meeran

Why awareness of cultural difference important? •  Global applicability of forecasting support system •  Awareness of culturally different ways of dealing uncertainty and decision making (e.g. situation in international commercial collaboration)

Judgmental Bias: Overconfidence •  Interval Judgment, i.e. to give an interval that you are 90% confident that true value will fall in the interval. •  Overconfidence reveals when: Prediction intervals are too narrow for the stated level of confidence

Cross Cultural Variations •  Probability Assessment: Stronger overconfidence is revealed in East Asian sample’s judgments. 1.  East Asian vs. British (Wright et al. 1980) 2.  Chinese vs. Americans (Yates et al. 1998)

Cross Cultural Variations •  Risk Taking Behaviour –  Risk Perception through investigating different dimensions of risk evaluation model Chinese probability of loss magnitude of loss

American More important

More Important

–  Risk Preference •  Chinese: Risk Taking •  Western: Risk Averse

Explanations? Cushion Hypothesis (?): Chinese people can afford to take more financial risks because their social network is generally larger in scale compared to Americans, and is also more willing to lend them support in case they need it. Therefore, the social network is like a “cushion” that holds the members if they “fall”.

Would the above findings be generalised into judgmental interval forecasting? If so, what’s the reason behind it?

Research Questions •  To what extent is overconfidence associated with judgmental forecasts when the forecasts are expressed as interval forecasts? •  To what extent does the degree of overconfidence differ between forecasters from Chinese and Western cultures?

Hypothesis •  H1 - Chinese people exhibit greater overconfidence compared to Western people in interval forecasting, that is, Chinese people’s prediction intervals will be narrower than those of Western people for a given coverage probability.

Experiment Instrument •  Sample: –  Master Student in Management School

–  Chinese: 540; British: 432

•  Experiment Material: Ø  Regression-simulated time series graphs: 12 annual product sales time series Ø Time series graphs consisted of up, flat and down trends, and low and high levels of noises.

Measurements •  Interval Width Mis-calibration Rate = (Judgmental – Regression)/Regression×100 -  < 0 implies Overconfidence -  > 0 implies Underconfidence

•  Hit-rate: the percentage of actual sales observations that fall within the judgmental prediction intervals (e.g. perfect calibration of a 95% prediction interval this rate will be 95%)

Findings Cultural Variations - Chinese participants were found more overconfident in prediction interval judgments, in terms of: •  Mis-calibration rate –  𝜒2 (1,15)=4.52, p=0.033

•  Hit-rates –  𝜒2 (1,13)=6.2997, p=0.01208 Note: Difference in MAE is not significant.

Mis-Calibration Rate Comparison Across Trends -30.00

Up

Flat

Down

Mean Mis-Calibration Rate

-35.00

-39.87 -40.00

-40.49

-45.00

-49.27

-49.95

-50.00

-55.00

-48.95

British -57.74

Chinese -60.00

Trends

Hit-rates Comparisons Across Trends 1.00

88.72%

0.90

Hit-rates

0.80

78.46%

77.30% 78.98% 69.77%

0.70

59.76% 0.60

British Chinese

0.50 Up

Flat

Trends

Down

Mis-Calibration Rate Comparison Across Randomness -30.00

Low

Mean Mis-Calibration Rate

-35.00

High

-36.38 British

-40.00

Chinese -45.00

-47.41 -49.92 -50.00

-55.00

-57.14

-60.00

Level of Randomness

Hit-rates Across Levels of Randomness 0.90

0.85

82.91% 80.00%

Hit-rates

0.80

0.75

71.43% 68.08%

0.70

British

0.65

Chinese 0.60

Low

High

Level of Randomness

Other Findings •  Individual Differences – Sig. •  Forecasting task order - Sig. •  Trend – Sig. •  Level of Randomness – Sig. Interval Width Comparison (Randomness) Prediction Interval Width

70

50 40

Regression

58.8

60

Judgmental 39.2

30

27.9

24.19

20 10 0

Low

Randomness Level

High

Future Work

“Why?” Culturally difference in interpreting probability and forecasts? Cushion hypothesis generalisable? Difference in the degree of Anchoring?