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 48.45% per annum.
- MSFT price at the close of November 19, 2024 was $417.79 and was lower than the bottom border of the primary price channel by $61.66 (12.86%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.11% per annum.
- MSFT price at the close of November 19, 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 MSFT 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: September 13, 2022
End date: July 23, 2024
a = 4.2983
b = 0.0011
s = 0.0511
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 48.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0511) – 1
= 22.66%
September 13, 2022 calculations
Top border of price channel:
Exp(Y707)
= Exp(a + b × X707 + 2 × s)
= Exp(a + b × 1,028 + 2 × s)
= Exp(4.2983 + 0.0011 × 1,028 + 2 × 0.0511)
= Exp(5.5131)
= $247.93
Bottom border of price channel:
Exp(Y707)
= Exp(a + b × X707 – 2 × s)
= Exp(a + b × 1,028 – 2 × s)
= Exp(4.2983 + 0.0011 × 1,028 – 2 × 0.0511)
= Exp(5.3089)
= $202.12
July 23, 2024 calculations
Top border of price channel:
Exp(Y1,173)
= Exp(a + b × X1,173 + 2 × s)
= Exp(a + b × 1,707 + 2 × s)
= Exp(4.2983 + 0.0011 × 1,707 + 2 × 0.0511)
= Exp(6.2481)
= $517.04
Bottom border of price channel:
Exp(Y1,173)
= Exp(a + b × X1,173 – 2 × s)
= Exp(a + b × 1,707 – 2 × s)
= Exp(4.2983 + 0.0011 × 1,707 – 2 × 0.0511)
= Exp(6.0438)
= $421.50
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 48.45% per annum.
- MSFT price at the close of November 19, 2024 was $417.79 and was lower than the bottom border of the primary price channel by $61.66 (12.86%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 18, 2024
End date: November 19, 2024
a = 5.8104
b = 0.0001
s = 0.0345
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0345) – 1
= 14.81%
January 18, 2024 calculations
Top border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 + 2 × s)
= Exp(a + b × 1,520 + 2 × s)
= Exp(5.8104 + 0.0001 × 1,520 + 2 × 0.0345)
= Exp(6.0871)
= $440.12
Bottom border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 – 2 × s)
= Exp(a + b × 1,520 – 2 × s)
= Exp(5.8104 + 0.0001 × 1,520 – 2 × 0.0345)
= Exp(5.9490)
= $383.36
November 19, 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(5.8104 + 0.0001 × 1,826 + 2 × 0.0345)
= Exp(6.1288)
= $458.90
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.8104 + 0.0001 × 1,826 – 2 × 0.0345)
= Exp(5.9908)
= $399.72
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.11% per annum.
- MSFT price at the close of November 19, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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