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 30.75% per annum.
- LRCX price at the close of January 17, 2025 was $80.30 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 7.79% per annum.
- LRCX price at the close of January 17, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 LRCX 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: February 22, 2024
End date: January 16, 2025
a = 6.1179
b = -0.0010
s = 0.0778
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -30.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0778) – 1
= 36.50%
February 22, 2024 calculations
Top border of price channel:
Exp(Y1,029)
= Exp(a + b × X1,029 + 2 × s)
= Exp(a + b × 1,493 + 2 × s)
= Exp(6.1179 + -0.0010 × 1,493 + 2 × 0.0778)
= Exp(4.7702)
= $117.95
Bottom border of price channel:
Exp(Y1,029)
= Exp(a + b × X1,029 – 2 × s)
= Exp(a + b × 1,493 – 2 × s)
= Exp(6.1179 + -0.0010 × 1,493 – 2 × 0.0778)
= Exp(4.4591)
= $86.41
January 16, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(6.1179 + -0.0010 × 1,822 + 2 × 0.0778)
= Exp(4.4390)
= $84.69
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(6.1179 + -0.0010 × 1,822 – 2 × 0.0778)
= Exp(4.1278)
= $62.04
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 30.75% per annum.
- LRCX price at the close of January 17, 2025 was $80.30 and was inside the primary price channel.
Secondary Trend
Start date: October 15, 2024
End date: January 17, 2025
a = 3.9507
b = 0.0002
s = 0.0332
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 7.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0332) – 1
= 14.21%
October 15, 2024 calculations
Top border of price channel:
Exp(Y1,192)
= Exp(a + b × X1,192 + 2 × s)
= Exp(a + b × 1,729 + 2 × s)
= Exp(3.9507 + 0.0002 × 1,729 + 2 × 0.0332)
= Exp(4.3722)
= $79.22
Bottom border of price channel:
Exp(Y1,192)
= Exp(a + b × X1,192 – 2 × s)
= Exp(a + b × 1,729 – 2 × s)
= Exp(3.9507 + 0.0002 × 1,729 – 2 × 0.0332)
= Exp(4.2394)
= $69.36
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(3.9507 + 0.0002 × 1,823 + 2 × 0.0332)
= Exp(4.3915)
= $80.76
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(3.9507 + 0.0002 × 1,823 – 2 × 0.0332)
= Exp(4.2587)
= $70.72
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 7.79% per annum.
- LRCX price at the close of January 17, 2025 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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