Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 32.76% per annum.
- MMM price at the close of October 25, 2022 was $118.50 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 76.06% per annum.
- MMM price at the close of October 25, 2022 was higher than the top border of the secondary price channel by $1.25 (1.06%). This indicates a possible reversal in the secondary trend direction.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of MMM price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: May 5, 2021
End date: October 25, 2022
a = 6.7731
b = -0.0011
s = 0.0514
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -32.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0514) – 1
= 22.83%
May 5, 2021 calculations
Top border of price channel:
Exp(Y885)
= Exp(a + b × X885 + 2 × s)
= Exp(a + b × 1,287 + 2 × s)
= Exp(6.7731 + -0.0011 × 1,287 + 2 × 0.0514)
= Exp(5.4765)
= $239.01
Bottom border of price channel:
Exp(Y885)
= Exp(a + b × X885 – 2 × s)
= Exp(a + b × 1,287 – 2 × s)
= Exp(6.7731 + -0.0011 × 1,287 – 2 × 0.0514)
= Exp(5.2708)
= $194.58
October 25, 2022 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(6.7731 + -0.0011 × 1,825 + 2 × 0.0514)
= Exp(4.8915)
= $133.15
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.7731 + -0.0011 × 1,825 – 2 × 0.0514)
= Exp(4.6858)
= $108.40
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 32.76% per annum.
- MMM price at the close of October 25, 2022 was $118.50 and was inside the primary price channel.
Secondary Trend
Start date: July 29, 2022
End date: October 25, 2022
a = 11.8072
b = -0.0039
s = 0.0526
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0039) – 1
= -76.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0526) – 1
= 23.44%
July 29, 2022 calculations
Top border of price channel:
Exp(Y1,196)
= Exp(a + b × X1,196 + 2 × s)
= Exp(a + b × 1,737 + 2 × s)
= Exp(11.8072 + -0.0039 × 1,737 + 2 × 0.0526)
= Exp(5.1090)
= $165.50
Bottom border of price channel:
Exp(Y1,196)
= Exp(a + b × X1,196 – 2 × s)
= Exp(a + b × 1,737 – 2 × s)
= Exp(11.8072 + -0.0039 × 1,737 – 2 × 0.0526)
= Exp(4.8984)
= $134.08
October 25, 2022 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(11.8072 + -0.0039 × 1,825 + 2 × 0.0526)
= Exp(4.7643)
= $117.25
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(11.8072 + -0.0039 × 1,825 – 2 × 0.0526)
= Exp(4.5538)
= $94.99
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 76.06% per annum.
- MMM price at the close of October 25, 2022 was higher than the top border of the secondary price channel by $1.25 (1.06%). This indicates a possible reversal in the secondary trend direction.
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