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 33.69% per annum.
- MRK price at the close of November 4, 2024 was $101.87 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 65.56% per annum.
- MRK price at the close of November 4, 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 MRK 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: April 25, 2024
End date: November 4, 2024
a = 6.7283
b = -0.0011
s = 0.0308
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -33.69%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0308) – 1
= 13.10%
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,124)
= Exp(a + b × X1,124 + 2 × s)
= Exp(a + b × 1,633 + 2 × s)
= Exp(6.7283 + -0.0011 × 1,633 + 2 × 0.0308)
= Exp(4.9518)
= $141.43
Bottom border of price channel:
Exp(Y1,124)
= Exp(a + b × X1,124 – 2 × s)
= Exp(a + b × 1,633 – 2 × s)
= Exp(6.7283 + -0.0011 × 1,633 – 2 × 0.0308)
= Exp(4.8288)
= $125.05
November 4, 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(6.7283 + -0.0011 × 1,826 + 2 × 0.0308)
= Exp(4.7346)
= $113.82
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.7283 + -0.0011 × 1,826 – 2 × 0.0308)
= Exp(4.6115)
= $100.64
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 33.69% per annum.
- MRK price at the close of November 4, 2024 was $101.87 and was inside the primary price channel.
Secondary Trend
Start date: September 16, 2024
End date: November 4, 2024
a = 9.9596
b = -0.0029
s = 0.0118
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0029) – 1
= -65.56%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0118) – 1
= 4.82%
September 16, 2024 calculations
Top border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 + 2 × s)
= Exp(a + b × 1,777 + 2 × s)
= Exp(9.9596 + -0.0029 × 1,777 + 2 × 0.0118)
= Exp(4.7939)
= $120.77
Bottom border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 – 2 × s)
= Exp(a + b × 1,777 – 2 × s)
= Exp(9.9596 + -0.0029 × 1,777 – 2 × 0.0118)
= Exp(4.7469)
= $115.22
November 4, 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(9.9596 + -0.0029 × 1,826 + 2 × 0.0118)
= Exp(4.6508)
= $104.67
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(9.9596 + -0.0029 × 1,826 – 2 × 0.0118)
= Exp(4.6038)
= $99.86
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 65.56% per annum.
- MRK price at the close of November 4, 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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