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 75.27% per annum.
- LRCX price at the close of May 7, 2024 was $914.91 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 35.22% per annum.
- LRCX price at the close of May 7, 2024 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: September 15, 2022
End date: May 7, 2024
a = 4.0588
b = 0.0015
s = 0.0742
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 75.27%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0742) – 1
= 34.55%
September 15, 2022 calculations
Top border of price channel:
Exp(Y846)
= Exp(a + b × X846 + 2 × s)
= Exp(a + b × 1,226 + 2 × s)
= Exp(4.0588 + 0.0015 × 1,226 + 2 × 0.0742)
= Exp(6.0921)
= $442.36
Bottom border of price channel:
Exp(Y846)
= Exp(a + b × X846 – 2 × s)
= Exp(a + b × 1,226 – 2 × s)
= Exp(4.0588 + 0.0015 × 1,226 – 2 × 0.0742)
= Exp(5.7954)
= $328.77
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.0588 + 0.0015 × 1,826 + 2 × 0.0742)
= Exp(7.0146)
= $1,112.75
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.0588 + 0.0015 × 1,826 – 2 × 0.0742)
= Exp(6.7178)
= $827.02
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 75.27% per annum.
- LRCX price at the close of May 7, 2024 was $914.91 and was inside the primary price channel.
Secondary Trend
Start date: March 1, 2024
End date: May 7, 2024
a = 8.9784
b = -0.0012
s = 0.0314
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0012) – 1
= -35.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0314) – 1
= 13.37%
March 1, 2024 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,759 + 2 × s)
= Exp(8.9784 + -0.0012 × 1,759 + 2 × 0.0314)
= Exp(6.9487)
= $1,041.75
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,759 – 2 × s)
= Exp(8.9784 + -0.0012 × 1,759 – 2 × 0.0314)
= Exp(6.8232)
= $918.88
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(8.9784 + -0.0012 × 1,826 + 2 × 0.0314)
= Exp(6.8690)
= $961.94
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(8.9784 + -0.0012 × 1,826 – 2 × 0.0314)
= Exp(6.7435)
= $848.48
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 35.22% per annum.
- LRCX price at the close of May 7, 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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