Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 48.20% per annum.
- MSI price at the close of August 1, 2024 was $397.70 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 75.59% per annum.
- MSI price at the close of August 1, 2024 was inside the secondary price channel.
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 MSI 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: August 15, 2023
End date: August 1, 2024
a = 4.0069
b = 0.0011
s = 0.0271
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 48.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0271) – 1
= 11.44%
August 15, 2023 calculations
Top border of price channel:
Exp(Y1,015)
= Exp(a + b × X1,015 + 2 × s)
= Exp(a + b × 1,474 + 2 × s)
= Exp(4.0069 + 0.0011 × 1,474 + 2 × 0.0271)
= Exp(5.6498)
= $284.24
Bottom border of price channel:
Exp(Y1,015)
= Exp(a + b × X1,015 – 2 × s)
= Exp(a + b × 1,474 – 2 × s)
= Exp(4.0069 + 0.0011 × 1,474 – 2 × 0.0271)
= Exp(5.5415)
= $255.05
August 1, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.0069 + 0.0011 × 1,826 + 2 × 0.0271)
= Exp(6.0292)
= $415.40
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.0069 + 0.0011 × 1,826 – 2 × 0.0271)
= Exp(5.9209)
= $372.74
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 48.20% per annum.
- MSI price at the close of August 1, 2024 was $397.70 and was inside the primary price channel.
Secondary Trend
Start date: April 12, 2024
End date: August 1, 2024
a = 3.1808
b = 0.0015
s = 0.0148
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 75.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0148) – 1
= 6.12%
April 12, 2024 calculations
Top border of price channel:
Exp(Y1,181)
= Exp(a + b × X1,181 + 2 × s)
= Exp(a + b × 1,715 + 2 × s)
= Exp(3.1808 + 0.0015 × 1,715 + 2 × 0.0148)
= Exp(5.8558)
= $349.25
Bottom border of price channel:
Exp(Y1,181)
= Exp(a + b × X1,181 – 2 × s)
= Exp(a + b × 1,715 – 2 × s)
= Exp(3.1808 + 0.0015 × 1,715 – 2 × 0.0148)
= Exp(5.7964)
= $329.11
August 1, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.1808 + 0.0015 × 1,826 + 2 × 0.0148)
= Exp(6.0270)
= $414.47
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.1808 + 0.0015 × 1,826 – 2 × 0.0148)
= Exp(5.9676)
= $390.57
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 75.59% per annum.
- MSI price at the close of August 1, 2024 was inside the secondary price channel.
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